Society for Industrial and Applied Mathematics: Applied Geometry
Applied Geometry  New results matching your topic search.
https://epubs.siam.org/action/doSearch?af=R
Society for Industrial and Applied Mathematics: Applied Geometry
Society for Industrial and Applied Mathematics
enUS
Atypon Systems
http://www.atypon.com/images/atypon_logo_small.gif
http://www.atypon.com

Linear and Nonlinear Functional Analysis with Applications
https://epubs.siam.org/doi/book/10.1137/1.9781611972597?af=R
Linear and Nonlinear Functional Analysis with Applications. <br/>
Linear and Nonlinear Functional Analysis with Applications. <br/><p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2013/1.9781611972597/1.9781611972597/20230629/1.9781611972597.cover.jpg" alttext="cover image"/></p>
Linear and Nonlinear Functional Analysis with Applications
doi:10.1137/1.9781611972597
Philippe G. Ciarlet
Linear and Nonlinear Functional Analysis with Applications
20230629T07:00:00Z
10.1137/1.9781611972597
https://epubs.siam.org/doi/book/10.1137/1.9781611972597?af=R
© 2013 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones
https://epubs.siam.org/doi/book/10.1137/1.9781611976533?af=R
Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones. <br/> In recent years, the world of molecular biology has witnessed a technology explosion, the socalled omics revolution, which has opened windows into cellular metabolic potential and activity that have already revolutionized numerous subfields of biology and medicine. At the same time, this technology (genomics, transcriptomics, etc.), intrinsically through its very nature and extrinsically through its widespread use, has generated a lot of data that begs, and has received, much statistical and mathematical attention. Such data analysis is arguably as important, if not more so, than the measurements themselves; without the appropriate parsing, much of the information potential is inaccessible.
Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones. <br/> In recent years, the world of molecular biology has witnessed a technology explosion, the socalled omics revolution, which has opened windows into cellular metabolic potential and activity that have already revolutionized numerous subfields of biology and medicine. At the same time, this technology (genomics, transcriptomics, etc.), intrinsically through its very nature and extrinsically through its widespread use, has generated a lot of data that begs, and has received, much statistical and mathematical attention. Such data analysis is arguably as important, if not more so, than the measurements themselves; without the appropriate parsing, much of the information potential is inaccessible. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2021/1.9781611976533/1.9781611976533/20210617/1.9781611976533.cover.jpg" alttext="cover image"/></p>
Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones
doi:10.1137/1.9781611976533
Isaac Klapper
Daniel B. Szyld
Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones
20210617T07:46:43Z
10.1137/1.9781611976533
https://epubs.siam.org/doi/book/10.1137/1.9781611976533?af=R
© 2021 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Observability: A New Theory Based on the Group of Invariance
https://epubs.siam.org/doi/book/10.1137/1.9781611976250?af=R
Observability: A New Theory Based on the Group of Invariance. <br/> This book is the result of almost three decades of research in very different scientific and technological domains: robotics, computer vision, Brownian dynamics, astrophysics/cosmology, and neuroscience. From one side, my interest in observability originates from very practical exigencies. Specifically, for a long time, I studied the possibility of using monocular vision and inertial sensors to make a drone able to fly autonomously in challenging realworld scenarios, such as remote inspection and search and rescue after natural disasters. This made it necessary to develop sophisticated and robust estimation strategies able to work in real time. In this respect, I was forced to learn more and more on the theory of nonlinear observability, i.e., in order to design suitable methodologies for very complex estimation problems. From another side, my background and long experience in theoretical physics allowed me to look at the problem of observability from a completely different perspective, and to adopt methods that are original and, I believe, innovative with respect to the existing literature in control theory.
Observability: A New Theory Based on the Group of Invariance. <br/> This book is the result of almost three decades of research in very different scientific and technological domains: robotics, computer vision, Brownian dynamics, astrophysics/cosmology, and neuroscience. From one side, my interest in observability originates from very practical exigencies. Specifically, for a long time, I studied the possibility of using monocular vision and inertial sensors to make a drone able to fly autonomously in challenging realworld scenarios, such as remote inspection and search and rescue after natural disasters. This made it necessary to develop sophisticated and robust estimation strategies able to work in real time. In this respect, I was forced to learn more and more on the theory of nonlinear observability, i.e., in order to design suitable methodologies for very complex estimation problems. From another side, my background and long experience in theoretical physics allowed me to look at the problem of observability from a completely different perspective, and to adopt methods that are original and, I believe, innovative with respect to the existing literature in control theory. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/dc/2020/1.9781611976250/1.9781611976250/20200825/1.9781611976250.cover.jpg" alttext="cover image"/></p>
Observability: A New Theory Based on the Group of Invariance
doi:10.1137/1.9781611976250
Agostino Martinelli
Observability: A New Theory Based on the Group of Invariance
20200825T07:11:46Z
10.1137/1.9781611976250
https://epubs.siam.org/doi/book/10.1137/1.9781611976250?af=R
© 2020 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Approximation and Modeling with BSplines
https://epubs.siam.org/doi/book/10.1137/1.9781611972955?af=R
Approximation and Modeling with BSplines. <br/> Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulations. Because of their computational efficiency, flexibility, and elegance, Bspline techniques are much superior to other, more elementary, piecewise polynomial representations. As a consequence, they have become the method of choice in numerous branches of applied mathematics, computer science, and engineering.
Approximation and Modeling with BSplines. <br/> Bsplines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulations. Because of their computational efficiency, flexibility, and elegance, Bspline techniques are much superior to other, more elementary, piecewise polynomial representations. As a consequence, they have become the method of choice in numerous branches of applied mathematics, computer science, and engineering. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2013/1.9781611972955/1.9781611972955/20191217/1.9781611972955.cover.jpg" alttext="cover image"/></p>
Approximation and Modeling with BSplines
doi:10.1137/1.9781611972955
Klaus Höllig
Jörg Hörner
Approximation and Modeling with BSplines
20191217T08:25:03Z
10.1137/1.9781611972955
https://epubs.siam.org/doi/book/10.1137/1.9781611972955?af=R
© 2013 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Numerically Solving Polynomial Systems with Bertini
https://epubs.siam.org/doi/book/10.1137/1.9781611972702?af=R
Numerically Solving Polynomial Systems with Bertini. <br/> Systems of polynomial equations are a common occurrence in problem formulations in engineering, science, and mathematics. Solution sets of such systems, i.e., algebraic sets, are wellbehaved, and effective algorithms have been developed in recent years to numerically compute and manipulate them. This field is called numerical algebraic geometry. Moreover, there is free software implementing these algorithms both for single computers and for computer clusters. As the developers of Bertini [22], we focus on this opensource software package in this book.
Numerically Solving Polynomial Systems with Bertini. <br/> Systems of polynomial equations are a common occurrence in problem formulations in engineering, science, and mathematics. Solution sets of such systems, i.e., algebraic sets, are wellbehaved, and effective algorithms have been developed in recent years to numerically compute and manipulate them. This field is called numerical algebraic geometry. Moreover, there is free software implementing these algorithms both for single computers and for computer clusters. As the developers of Bertini [22], we focus on this opensource software package in this book. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/se/2013/1.9781611972702/1.9781611972702/20191216/1.9781611972702.cover.jpg" alttext="cover image"/></p>
Numerically Solving Polynomial Systems with Bertini
doi:10.1137/1.9781611972702
Daniel J. Bates
Andrew J. Sommese
Jonathan D. Hauenstein
Charles W. Wampler
Numerically Solving Polynomial Systems with Bertini
20191216T02:49:02Z
10.1137/1.9781611972702
https://epubs.siam.org/doi/book/10.1137/1.9781611972702?af=R
© 2013 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Piecewise Affine Control: ContinuousTime, Sampled Data, and Networked Systems
https://epubs.siam.org/doi/book/10.1137/1.9781611975901?af=R
Piecewise Affine Control: ContinuousTime, Sampled Data, and Networked Systems. <br/> This book is about the analysis and synthesis of controllers for piecewise affine systems. Piecewise affine systems are a modeling class that is very powerful for both switched and nonlinear dynamics. It finds applications in many areas, including, but not limited to, switching electronic circuits, disk drives, robotic systems, autonomous vehicles, chemical reactors, climate change models, neural networks, and biological systems. The book provides Lyapunov dissipativitybased methodologies that tackle sliding modes, which is an important concern in continuoustime piecewise affine systems. The importance of handling sliding modes is twofold. First, sliding modes are usually present without one necessarily being able to predict their occurrence at the modeling stage. Therefore, any analysis or synthesis method that is not inclusive of sliding modes might simply give an erroneous conclusion about stability or performance. Second, sliding modes can sometimes be beneficial if they are convergent. Therefore, a controller synthesis methodology that naturally handles sliding modes might be less conservative because it does not try to spend control effort eliminating them when they are not harmful.
Piecewise Affine Control: ContinuousTime, Sampled Data, and Networked Systems. <br/> This book is about the analysis and synthesis of controllers for piecewise affine systems. Piecewise affine systems are a modeling class that is very powerful for both switched and nonlinear dynamics. It finds applications in many areas, including, but not limited to, switching electronic circuits, disk drives, robotic systems, autonomous vehicles, chemical reactors, climate change models, neural networks, and biological systems. The book provides Lyapunov dissipativitybased methodologies that tackle sliding modes, which is an important concern in continuoustime piecewise affine systems. The importance of handling sliding modes is twofold. First, sliding modes are usually present without one necessarily being able to predict their occurrence at the modeling stage. Therefore, any analysis or synthesis method that is not inclusive of sliding modes might simply give an erroneous conclusion about stability or performance. Second, sliding modes can sometimes be beneficial if they are convergent. Therefore, a controller synthesis methodology that naturally handles sliding modes might be less conservative because it does not try to spend control effort eliminating them when they are not harmful. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/dc/2019/1.9781611975901/1.9781611975901/20191107/1.9781611975901.cover.jpg" alttext="cover image"/></p>
Piecewise Affine Control: ContinuousTime, Sampled Data, and Networked Systems
doi:10.1137/1.9781611975901
Luis Rodrigues
Behzad Samadi
Miad Moarref
Piecewise Affine Control: ContinuousTime, Sampled Data, and Networked Systems
20191107T05:08:49Z
10.1137/1.9781611975901
https://epubs.siam.org/doi/book/10.1137/1.9781611975901?af=R
© 2020 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

The Shapes of Things
https://epubs.siam.org/doi/book/10.1137/1.9781611973969?af=R
The Shapes of Things. <br/> Form follows function. This old adage from art and architecture, credited to American architect Louis H. Sullivan, holds true. The shape of an object is intimately connected to its purpose. Nature provides many examples of this: the shape of a tree and its leaves to harvest light, the wings of a bird to fly, the body of a snake to slither, and the structure of the human heart to keep us alive. So good is this rubric that it finds application inmodern design principles, e.g., the shapes of tools, the profile of an automobile, and the design of a bridge.
The Shapes of Things. <br/> Form follows function. This old adage from art and architecture, credited to American architect Louis H. Sullivan, holds true. The shape of an object is intimately connected to its purpose. Nature provides many examples of this: the shape of a tree and its leaves to harvest light, the wings of a bird to fly, the body of a snake to slither, and the structure of the human heart to keep us alive. So good is this rubric that it finds application inmodern design principles, e.g., the shapes of tools, the profile of an automobile, and the design of a bridge. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/dc/2015/1.9781611973969/1.9781611973969/20150625/1.9781611973969.cover.jpg" alttext="cover image"/></p>
The Shapes of Things
doi:10.1137/1.9781611973969
Shawn W. Walker
The Shapes of Things
20150625T06:25:11Z
10.1137/1.9781611973969
https://epubs.siam.org/doi/book/10.1137/1.9781611973969?af=R
© 2015 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Nonlinear Time Scale Systems in Standard and Nonstandard Forms
https://epubs.siam.org/doi/book/10.1137/1.9781611973341?af=R
Nonlinear Time Scale Systems in Standard and Nonstandard Forms. <br/> Singular perturbation theory plays a significant role in analysis and design of control laws. It presents control engineers with the advantage of model reduction that simplifies both the software and hardware implementation of control algorithms. Through this book, our goal is to present the reader with control design techniques that extend these benefits to a larger class of systems, specifically to those that are not traditionally controlled through this methodology. Our aim in doing so is to show the reader that some classes of nonminimum phase control problems can be actively controlled in realtime through use of singular perturbation methods.
Nonlinear Time Scale Systems in Standard and Nonstandard Forms. <br/> Singular perturbation theory plays a significant role in analysis and design of control laws. It presents control engineers with the advantage of model reduction that simplifies both the software and hardware implementation of control algorithms. Through this book, our goal is to present the reader with control design techniques that extend these benefits to a larger class of systems, specifically to those that are not traditionally controlled through this methodology. Our aim in doing so is to show the reader that some classes of nonminimum phase control problems can be actively controlled in realtime through use of singular perturbation methods. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/dc/2014/1.9781611973341/1.9781611973341/20140502/1.9781611973341.cover.jpg" alttext="cover image"/></p>
Nonlinear Time Scale Systems in Standard and Nonstandard Forms
doi:10.1137/1.9781611973341
Anshu NarangSiddarth
John Valasek
Nonlinear Time Scale Systems in Standard and Nonstandard Forms
20140502T02:00:16Z
10.1137/1.9781611973341
https://epubs.siam.org/doi/book/10.1137/1.9781611973341?af=R
© 2014 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Knot Insertion and Deletion Algorithms for BSpline Curves and Surfaces
https://epubs.siam.org/doi/book/10.1137/1.9781611971583?af=R
Knot Insertion and Deletion Algorithms for BSpline Curves and Surfaces. <br/> Knot insertion and deletion algorithms are the two fundamental procedures needed for understanding, analyzing, and rendering Bspline curves and surfaces. This approach to splines, however, is not traditional; originally divided differences were used to develop almost all of the theory of univariate Bsplines. This point of view began to change in the mid1970s with the publication of the Coxde BoorMansfield recurrence. Many computer scientists and engineers not familiar with divided differences wanted to apply splines to computer graphics and computer aided design; this recurrence provided a much easier entry for them into the subject. Since this recurrence is numerically stable, it lends itself very naturally to computer programming, and therefore, as well, to computer aided design.
Knot Insertion and Deletion Algorithms for BSpline Curves and Surfaces. <br/> Knot insertion and deletion algorithms are the two fundamental procedures needed for understanding, analyzing, and rendering Bspline curves and surfaces. This approach to splines, however, is not traditional; originally divided differences were used to develop almost all of the theory of univariate Bsplines. This point of view began to change in the mid1970s with the publication of the Coxde BoorMansfield recurrence. Many computer scientists and engineers not familiar with divided differences wanted to apply splines to computer graphics and computer aided design; this recurrence provided a much easier entry for them into the subject. Since this recurrence is numerically stable, it lends itself very naturally to computer programming, and therefore, as well, to computer aided design. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/1992/1.9781611971583/1.9781611971583/20140213/1.9781611971583.cover.jpg" alttext="cover image"/></p>
Knot Insertion and Deletion Algorithms for BSpline Curves and Surfaces
doi:10.1137/1.9781611971583
Knot Insertion and Deletion Algorithms for BSpline Curves and Surfaces
20140213T07:30:02Z
10.1137/1.9781611971583
https://epubs.siam.org/doi/book/10.1137/1.9781611971583?af=R
© 1993 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the Publisher. For information, write the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 191042688.

Topics in Surface Modeling
https://epubs.siam.org/doi/book/10.1137/1.9781611971644?af=R
Topics in Surface Modeling. <br/> Curve and surface design methods have grown increasingly sophisticated over the last 30 years. This book contains new ideas and results in three areas of growth: algebraic methods, variational surface design, and special applications. It is intended for practical, industrial applications, as well as research in academic environments.
Topics in Surface Modeling. <br/> Curve and surface design methods have grown increasingly sophisticated over the last 30 years. This book contains new ideas and results in three areas of growth: algebraic methods, variational surface design, and special applications. It is intended for practical, industrial applications, as well as research in academic environments. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/1992/1.9781611971644/1.9781611971644/20140213/1.9781611971644.cover.jpg" alttext="cover image"/></p>
Topics in Surface Modeling
doi:10.1137/1.9781611971644
Topics in Surface Modeling
20140213T07:27:02Z
10.1137/1.9781611971644
https://epubs.siam.org/doi/book/10.1137/1.9781611971644?af=R
© 1992 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the Publisher. For information, write the Society for Industrial and Applied Mathematics, 3600 University City Science Center, Philadelphia, PA 191042688.

The Radon Transform and Medical Imaging
https://epubs.siam.org/doi/book/10.1137/1.9781611973297?af=R
The Radon Transform and Medical Imaging. <br/> This text addresses the topics covered in ten lectures delivered by the author during the 2012 CBMSNSF conference “Mathematical methods of computed tomography.” The goals of the lectures were to describe the main problems and techniques of some wellestablished imaging modalities, to emphasize the most important mathematical ideas involved, and to give a brief overview of several imaging techniques that are less common and/or currently being developed.
The Radon Transform and Medical Imaging. <br/> This text addresses the topics covered in ten lectures delivered by the author during the 2012 CBMSNSF conference “Mathematical methods of computed tomography.” The goals of the lectures were to describe the main problems and techniques of some wellestablished imaging modalities, to emphasize the most important mathematical ideas involved, and to give a brief overview of several imaging techniques that are less common and/or currently being developed. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/cb/2013/1.9781611973297/1.9781611973297/20140127/1.9781611973297.cover.jpg" alttext="cover image"/></p>
The Radon Transform and Medical Imaging
doi:10.1137/1.9781611973297
Peter Kuchment
The Radon Transform and Medical Imaging
20140127T09:14:23Z
10.1137/1.9781611973297
https://epubs.siam.org/doi/book/10.1137/1.9781611973297?af=R
© 2014 by the Society for Industrial and Applied MathematicsAll rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, 6th Floor, Philadelphia, PA 191042688 USA.

Introduction to the Mathematics of Subdivision Surfaces
https://epubs.siam.org/doi/book/10.1137/1.9780898717617?af=R
Introduction to the Mathematics of Subdivision Surfaces. <br/> Subdivision surfaces were introduced in the ComputerAided Design (CAD) literature in the late 1970s, and they have since attracted much attention in the fields of computer graphics, solid modelling, and computeraided geometric design. It is the purpose of this book to introduce the essential mathematics underlying these surfaces, at a level that is accessible both to graduate students in computer science and to researchers and practitioners with a similar or stronger mathematical background. In terms of mathematical content, the book has two main goals. The first is to provide a unified view of the field. The second is to explain the mathematics carefully, but as simply as possible, so that the reader will be able to easily read the literature.
Introduction to the Mathematics of Subdivision Surfaces. <br/> Subdivision surfaces were introduced in the ComputerAided Design (CAD) literature in the late 1970s, and they have since attracted much attention in the fields of computer graphics, solid modelling, and computeraided geometric design. It is the purpose of this book to introduce the essential mathematics underlying these surfaces, at a level that is accessible both to graduate students in computer science and to researchers and practitioners with a similar or stronger mathematical background. In terms of mathematical content, the book has two main goals. The first is to provide a unified view of the field. The second is to explain the mathematics carefully, but as simply as possible, so that the reader will be able to easily read the literature. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2010/1.9780898717617/1.9780898717617/production/1.9780898717617.cover.jpg" alttext="cover image"/></p>
Introduction to the Mathematics of Subdivision Surfaces
doi:10.1137/1.9780898717617
LarsErik Andersson
Neil F. Stewart
Introduction to the Mathematics of Subdivision Surfaces
20120525T07:11:18Z
10.1137/1.9780898717617
https://epubs.siam.org/doi/book/10.1137/1.9780898717617?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Symmetry in Chaos
https://epubs.siam.org/doi/book/10.1137/1.9780898717709?af=R
Symmetry in Chaos. <br/> Since the publication of Symmetry in Chaos in 1992, substantial progress has been made on the mathematics and science underlying symmetric chaos. For example, the concept of patterns on average is based on the mathematics behind our symmetric images. Bruce Gluckman, Philippe Marcq, Josh Bridger, and Jerry Gollub conducted elegant experiments at Haverford College which show that patterns on average occur in the Faraday experiment—a classical experiment from fluid dynamics. We have described this experiment in the revised introductory chapter. On the mathematical side, attractor symmetries have been classified and methods for numerically determining the symmetry of higher dimensional analogues of our images have been developed. The mathematical results have been obtained in collaboration with Pete Ashwin, Ernie Barany, Michael Dellnitz, Ian Melbourne, and Matt Nicol. In another direction, the increasing power of desktop computers has enabled significant improvement of the resolution of the images as well as improvements in the coloring algorithms. Although, with few exceptions, we have kept the computergenerated images shown in the first edition, we have tried to improve both the quality and coloring of the images. We have added one or two new pictures, mainly in Chapters 4 and 5, which we hope will make some of the mathematical explanations of chaos easier to read. Aside from the changes mentioned above, we replaced a few of the nonmathematical images. We have also worked to improve some of the mathematical explanations and have made minor improvements throughout the text. We removed the appendix on Basic programs—since Basic is no longer a readily available or widely used computer language.
Symmetry in Chaos. <br/> Since the publication of Symmetry in Chaos in 1992, substantial progress has been made on the mathematics and science underlying symmetric chaos. For example, the concept of patterns on average is based on the mathematics behind our symmetric images. Bruce Gluckman, Philippe Marcq, Josh Bridger, and Jerry Gollub conducted elegant experiments at Haverford College which show that patterns on average occur in the Faraday experiment—a classical experiment from fluid dynamics. We have described this experiment in the revised introductory chapter. On the mathematical side, attractor symmetries have been classified and methods for numerically determining the symmetry of higher dimensional analogues of our images have been developed. The mathematical results have been obtained in collaboration with Pete Ashwin, Ernie Barany, Michael Dellnitz, Ian Melbourne, and Matt Nicol. In another direction, the increasing power of desktop computers has enabled significant improvement of the resolution of the images as well as improvements in the coloring algorithms. Although, with few exceptions, we have kept the computergenerated images shown in the first edition, we have tried to improve both the quality and coloring of the images. We have added one or two new pictures, mainly in Chapters 4 and 5, which we hope will make some of the mathematical explanations of chaos easier to read. Aside from the changes mentioned above, we replaced a few of the nonmathematical images. We have also worked to improve some of the mathematical explanations and have made minor improvements throughout the text. We removed the appendix on Basic programs—since Basic is no longer a readily available or widely used computer language. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2009/1.9780898717709/1.9780898717709/production/1.9780898717709.cover.jpg" alttext="cover image"/></p>
Symmetry in Chaos
doi:10.1137/1.9780898717709
Michael Field
Martin Golubitsky
Symmetry in Chaos
20120525T07:09:37Z
10.1137/1.9780898717709
https://epubs.siam.org/doi/book/10.1137/1.9780898717709?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

The SIAM 100Digit Challenge
https://epubs.siam.org/doi/book/10.1137/1.9780898717969?af=R
The SIAM 100Digit Challenge. <br/> This book will take you on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. A first unusual feature is that the tour is organized by problems, not methods : it is extremely valuable to realize that numerical problems often yield to a wide variety of methods. For example, we solve a randomwalk problem (Chapter 6) by several different techniques, such as largescale linear algebra, a threeterm recursion obtained by symbolic computations, elliptic integrals and the arithmeticgeometric mean, and Fourier analysis. We do so in IEEE arithmetic to full accuracy and, at the extreme, in highprecision arithmetic to get 10,000 digits. A second unusual feature is that we very carefully try to justify the validity of every single digit of a numerical answer, using methods ranging from carefully designed computer experiments and a posteriori error estimates to computerassisted proofs based on interval arithmetic. In the real world, the first two methods are usually adequate and give the desired confidence in the answer. Interval methods, while nicely rigorous, would most often not provide any additional benefit. Yet it sometimes happens that one of the best approaches to a problem is one that provides proof along the way (this occurs in Chapter 4), a point that has considerable mathematical interest. A main theme of the book is that there are usually two options for solving a numerical problem: either use a brute force method running overnight and unsupervised on a highperformance workstation with lots of memory, or spend your days thinking harder, with the help of mathematical theory and a good library, in the hope of coming up with a clever method that will solve the problem in less than a second on common hardware. Of course, in practice these two options of attacking a problem will scale differently with problem size and difficulty, and your choice will depend on such resources as your time, interest, and knowledge and the computer power at your disposal. One noteworthy case, where a detour guided by theory leads to an approach that is ultimately much more efficient than the direct path, is illustrated on the cover of this book. That diagram (taken from Chapter 1) illustrates that many problems about real numbers can be made much, much easier by stepping outside the real axis and taking a route through the complex plane.
The SIAM 100Digit Challenge. <br/> This book will take you on a thrilling tour of some of the most important and powerful areas of contemporary numerical mathematics. A first unusual feature is that the tour is organized by problems, not methods : it is extremely valuable to realize that numerical problems often yield to a wide variety of methods. For example, we solve a randomwalk problem (Chapter 6) by several different techniques, such as largescale linear algebra, a threeterm recursion obtained by symbolic computations, elliptic integrals and the arithmeticgeometric mean, and Fourier analysis. We do so in IEEE arithmetic to full accuracy and, at the extreme, in highprecision arithmetic to get 10,000 digits. A second unusual feature is that we very carefully try to justify the validity of every single digit of a numerical answer, using methods ranging from carefully designed computer experiments and a posteriori error estimates to computerassisted proofs based on interval arithmetic. In the real world, the first two methods are usually adequate and give the desired confidence in the answer. Interval methods, while nicely rigorous, would most often not provide any additional benefit. Yet it sometimes happens that one of the best approaches to a problem is one that provides proof along the way (this occurs in Chapter 4), a point that has considerable mathematical interest. A main theme of the book is that there are usually two options for solving a numerical problem: either use a brute force method running overnight and unsupervised on a highperformance workstation with lots of memory, or spend your days thinking harder, with the help of mathematical theory and a good library, in the hope of coming up with a clever method that will solve the problem in less than a second on common hardware. Of course, in practice these two options of attacking a problem will scale differently with problem size and difficulty, and your choice will depend on such resources as your time, interest, and knowledge and the computer power at your disposal. One noteworthy case, where a detour guided by theory leads to an approach that is ultimately much more efficient than the direct path, is illustrated on the cover of this book. That diagram (taken from Chapter 1) illustrates that many problems about real numbers can be made much, much easier by stepping outside the real axis and taking a route through the complex plane. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2004/1.9780898717969/1.9780898717969/production/1.9780898717969.cover.jpg" alttext="cover image"/></p>
The SIAM 100Digit Challenge
doi:10.1137/1.9780898717969
Folkmar Bornemann
Dirk Laurie
Stan Wagon
Jörg Waldvogel
The SIAM 100Digit Challenge
20120525T06:59:34Z
10.1137/1.9780898717969
https://epubs.siam.org/doi/book/10.1137/1.9780898717969?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Numerical Polynomial Algebra
https://epubs.siam.org/doi/book/10.1137/1.9780898717976?af=R
Numerical Polynomial Algebra. <br/> “Numerical Polynomial Algebra” is not a standard designation of a mathematical discipline; therefore, I should start by explaining the title of this book. Historically, in the growth of computational mathematics, which occurred in parallel with the breathtaking explosion in the performance of computational machinery, all areas of mathematics which play a role in the modelling and analysis of real world phenomena developed their branch of Numerical Analysis: Linear Algebra, Differential Equations, Approximation, Optimization, etc. The collective term Numerical Analysis turned out to be appropriate: The fact that data and relations from the real world inevitably have a limited accuracy make it necessary to embed the computational tasks into metric spaces: Few parts of computational scientific computing can proceed without approximations and without the analytic background (like norms, for example) to deal with the inherent indeterminations. Numerical Linear Algebra is the bestknown example: It originated from an embedding of the constructive parts of classical linear algebra into linear functional analysis, and its growth into one of the supporting pillars of scientific computing was driven by the use of analytic tools like mappings, norms, convergent iteration, etc. Empirical data could easily be fitted into this conceptual frame so that the approximate solution of approximate linear problems with approximate data could be conceived and implemented. One area of mathematics did not follow that trend: classical nonlinear algebra. It had undergone a remarkable algorithmic development in the late 19th century; then the axiomatic age had turned it into an abstract discipline. When the symbol manipulation capabilities of electronic computers became evident, a faction of algebraists remembered the algorithmic aspects of their field and developed them into “Computer Algebra,” as a computational tool for the solution of constructive problems in pure mathematics. They have designed and implemented algorithms which delight the algebraic community; but at the same time, this enterprise has somehow prevented the growth of a numerical nonlinear algebra. The inadequacy of this mathematically interesting project for realistic problems is exposed when the solution of a system of linear equations with numerical coefficients is obtained in the form of fractions of integers with hundreds of digits.
Numerical Polynomial Algebra. <br/> “Numerical Polynomial Algebra” is not a standard designation of a mathematical discipline; therefore, I should start by explaining the title of this book. Historically, in the growth of computational mathematics, which occurred in parallel with the breathtaking explosion in the performance of computational machinery, all areas of mathematics which play a role in the modelling and analysis of real world phenomena developed their branch of Numerical Analysis: Linear Algebra, Differential Equations, Approximation, Optimization, etc. The collective term Numerical Analysis turned out to be appropriate: The fact that data and relations from the real world inevitably have a limited accuracy make it necessary to embed the computational tasks into metric spaces: Few parts of computational scientific computing can proceed without approximations and without the analytic background (like norms, for example) to deal with the inherent indeterminations. Numerical Linear Algebra is the bestknown example: It originated from an embedding of the constructive parts of classical linear algebra into linear functional analysis, and its growth into one of the supporting pillars of scientific computing was driven by the use of analytic tools like mappings, norms, convergent iteration, etc. Empirical data could easily be fitted into this conceptual frame so that the approximate solution of approximate linear problems with approximate data could be conceived and implemented. One area of mathematics did not follow that trend: classical nonlinear algebra. It had undergone a remarkable algorithmic development in the late 19th century; then the axiomatic age had turned it into an abstract discipline. When the symbol manipulation capabilities of electronic computers became evident, a faction of algebraists remembered the algorithmic aspects of their field and developed them into “Computer Algebra,” as a computational tool for the solution of constructive problems in pure mathematics. They have designed and implemented algorithms which delight the algebraic community; but at the same time, this enterprise has somehow prevented the growth of a numerical nonlinear algebra. The inadequacy of this mathematically interesting project for realistic problems is exposed when the solution of a system of linear equations with numerical coefficients is obtained in the form of fractions of integers with hundreds of digits. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/ot/2004/1.9780898717976/1.9780898717976/production/1.9780898717976.cover.jpg" alttext="cover image"/></p>
Numerical Polynomial Algebra
doi:10.1137/1.9780898717976
Hans J. Stetter
Numerical Polynomial Algebra
20120525T06:59:50Z
10.1137/1.9780898717976
https://epubs.siam.org/doi/book/10.1137/1.9780898717976?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems
https://epubs.siam.org/doi/book/10.1137/1.9780898719031?af=R
Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems. <br/> This is an introduction to “polynomial continuation,” which is used to compute the solutions to systems of polynomial equations. The book shows how to solve practical problems but maintains an elementary mathematical perspective. The first two chapters illustrate most of the important concepts and numerical processes, using only highschool mathematics and some simple computer programs. Since 1987, when the book was first published, the field has advanced through many developments, noted below. Still, I have been gratified that students continue to take the trouble to let me know that they have found this book a useful starting point. The concrete, empirical, and conversational style of this book arose from my experiences as a mathematician at General Motors working with engineers. They sometimes were not convinced by proofs, but their mechanical intuition responded well to numerical experiments that demonstrated the “feel” of the concepts. I learned at this time the paradox that a verbal explanation can defeat its purpose, if made to a tactile person, no matter how correct the explanation, no matter how skilled the person. Consequently, the language in this book stays as basic as possible for as long as possible: subscripts are not used until the end of Chapter 2, the only “spaces” referenced are Euclidean, and no concept or computer code is more general than needed. Yet, the mathematical facts are complete and proven, not necessarily when they are introduced, but eventually. For this, I have relied on a few results from differential topology, avoiding more abstract mathematics. Carrying out the numerical exercises using the Fortran code provided is important to the learning experience of the book.
Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems. <br/> This is an introduction to “polynomial continuation,” which is used to compute the solutions to systems of polynomial equations. The book shows how to solve practical problems but maintains an elementary mathematical perspective. The first two chapters illustrate most of the important concepts and numerical processes, using only highschool mathematics and some simple computer programs. Since 1987, when the book was first published, the field has advanced through many developments, noted below. Still, I have been gratified that students continue to take the trouble to let me know that they have found this book a useful starting point. The concrete, empirical, and conversational style of this book arose from my experiences as a mathematician at General Motors working with engineers. They sometimes were not convinced by proofs, but their mechanical intuition responded well to numerical experiments that demonstrated the “feel” of the concepts. I learned at this time the paradox that a verbal explanation can defeat its purpose, if made to a tactile person, no matter how correct the explanation, no matter how skilled the person. Consequently, the language in this book stays as basic as possible for as long as possible: subscripts are not used until the end of Chapter 2, the only “spaces” referenced are Euclidean, and no concept or computer code is more general than needed. Yet, the mathematical facts are complete and proven, not necessarily when they are introduced, but eventually. For this, I have relied on a few results from differential topology, avoiding more abstract mathematics. Carrying out the numerical exercises using the Fortran code provided is important to the learning experience of the book. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/cl/2009/1.9780898719031/1.9780898719031/production/1.9780898719031.cover.jpg" alttext="cover image"/></p>
Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems
doi:10.1137/1.9780898719031
Alexander Morgan
Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems
20120525T06:04:09Z
10.1137/1.9780898719031
https://epubs.siam.org/doi/book/10.1137/1.9780898719031?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Shapes and Geometries
https://epubs.siam.org/doi/book/10.1137/1.9780898719826?af=R
Shapes and Geometries. <br/> 1 Objectives and Scope of the Book The objective of this book is to give a comprehensive presentation of mathematical constructions and tools that can be used to study problems where the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. In that context, a good analytical framework and good modeling techniques must be able to handle the occurrence of singular behaviors whenever they are compatible with the mechanics or the physics of the problems at hand. In some optimization problems, the natural intuitive notion of a geometric domain undergoes mutations into relaxed entities such as microstructures. So the objects under consideration need not be smooth open domains, or even sets, as long as they still makes sense mathematically. This book covers the basic mathematical ideas, constructions, and methods that come from different fields of mathematical activities and areas of applications that have often evolved in parallel directions. The scope of research is frighteningly broad because it touches on areas that include classical geometry, modern partial differential equations, geometric measure theory, topological groups, and constrained optimization, with applications to classical mechanics of continuous media such as fluid mechanics, elasticity theory, fracture theory, modern theories of optimal design, optimal location and shape of geometric objects, free and moving boundary problems, and image processing. Innovative modeling or new issues raised in some applications force a new look at the fundamentals of wellestablished mathematical areas such as geometry, to relax basic notions of volume, perimeter, and curvature or boundary value problems, and to find suitable relaxations of solutions. In that spirit, Henri Lebesgue was probably a pioneer when he relaxed the intuitive notion of volume to the one of measure on an equivalence class of measurable sets in 1907. He was followed in that endeavor in the early 1950s by the celebrated work of E. De Giorgi, who used the relaxed notion of perimeter defined on the class of Caccioppoli sets to solve Plateau's problem of minimal surfaces. The material that is pertinent to the study of geometric objects and the entities and functions that are defined on them would necessitate an encyclopedic investment to bring together the basic theories and their fields of applications. This objective is obviously beyond the scope of a single book and two authors.
Shapes and Geometries. <br/> 1 Objectives and Scope of the Book The objective of this book is to give a comprehensive presentation of mathematical constructions and tools that can be used to study problems where the modeling, optimization, or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. In that context, a good analytical framework and good modeling techniques must be able to handle the occurrence of singular behaviors whenever they are compatible with the mechanics or the physics of the problems at hand. In some optimization problems, the natural intuitive notion of a geometric domain undergoes mutations into relaxed entities such as microstructures. So the objects under consideration need not be smooth open domains, or even sets, as long as they still makes sense mathematically. This book covers the basic mathematical ideas, constructions, and methods that come from different fields of mathematical activities and areas of applications that have often evolved in parallel directions. The scope of research is frighteningly broad because it touches on areas that include classical geometry, modern partial differential equations, geometric measure theory, topological groups, and constrained optimization, with applications to classical mechanics of continuous media such as fluid mechanics, elasticity theory, fracture theory, modern theories of optimal design, optimal location and shape of geometric objects, free and moving boundary problems, and image processing. Innovative modeling or new issues raised in some applications force a new look at the fundamentals of wellestablished mathematical areas such as geometry, to relax basic notions of volume, perimeter, and curvature or boundary value problems, and to find suitable relaxations of solutions. In that spirit, Henri Lebesgue was probably a pioneer when he relaxed the intuitive notion of volume to the one of measure on an equivalence class of measurable sets in 1907. He was followed in that endeavor in the early 1950s by the celebrated work of E. De Giorgi, who used the relaxed notion of perimeter defined on the class of Caccioppoli sets to solve Plateau's problem of minimal surfaces. The material that is pertinent to the study of geometric objects and the entities and functions that are defined on them would necessitate an encyclopedic investment to bring together the basic theories and their fields of applications. This objective is obviously beyond the scope of a single book and two authors. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/dc/2011/1.9780898719826/1.9780898719826/production/1.9780898719826.cover.jpg" alttext="cover image"/></p>
Shapes and Geometries
doi:10.1137/1.9780898719826
M. C. Delfour
J. P. Zolésio
Shapes and Geometries
20120525T06:17:14Z
10.1137/1.9780898719826
https://epubs.siam.org/doi/book/10.1137/1.9780898719826?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Mathematical Aspects of Geometric Modeling
https://epubs.siam.org/doi/book/10.1137/1.9781611970067?af=R
Mathematical Aspects of Geometric Modeling. <br/> Less is more  more or less Ludwig Mies van der Rohe During the week of December 17–21, 1990 we presented a series of ten lectures on “Curves and Surfaces: An Algorithmic Viewpoint” at Kent State University under the auspice of the CBMS. When we began to write these lecture notes it became clear to us that anything more than a superficial description of concepts and results would lead to an inappropriately long monograph. Hence we decided that it would be better to choose only a portion of the lectures to elaborate on in detail. For these lectures we would strive for completeness so that the reader could minimize the inconvenience of consulting original sources for details. Each of the five chapters of this monograph contains introductory material followed by more advanced results. In retrospect, the selection of lectures reflects our fondness for spline functions. This was, in no small measure, the result of our attendance at a CBMS lecture on this subject given by I.J. Schoenberg in 1971. His inspirational lectures have influenced much of our own research and hence also this monograph. Fading memory always makes it hard to remember the origin of mathematical ideas, but certainly we haven't forgotten our debt of gratitude to our many collaborators. They represent an impressive group of talented mathematicians who have given generously of their time to patiently educate us. Much of the insights and contributions contained in this monograph are due to their efforts.
Mathematical Aspects of Geometric Modeling. <br/> Less is more  more or less Ludwig Mies van der Rohe During the week of December 17–21, 1990 we presented a series of ten lectures on “Curves and Surfaces: An Algorithmic Viewpoint” at Kent State University under the auspice of the CBMS. When we began to write these lecture notes it became clear to us that anything more than a superficial description of concepts and results would lead to an inappropriately long monograph. Hence we decided that it would be better to choose only a portion of the lectures to elaborate on in detail. For these lectures we would strive for completeness so that the reader could minimize the inconvenience of consulting original sources for details. Each of the five chapters of this monograph contains introductory material followed by more advanced results. In retrospect, the selection of lectures reflects our fondness for spline functions. This was, in no small measure, the result of our attendance at a CBMS lecture on this subject given by I.J. Schoenberg in 1971. His inspirational lectures have influenced much of our own research and hence also this monograph. Fading memory always makes it hard to remember the origin of mathematical ideas, but certainly we haven't forgotten our debt of gratitude to our many collaborators. They represent an impressive group of talented mathematicians who have given generously of their time to patiently educate us. Much of the insights and contributions contained in this monograph are due to their efforts. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/cb/1995/1.9781611970067/1.9781611970067/production/1.9781611970067.cover.jpg" alttext="cover image"/></p>
Mathematical Aspects of Geometric Modeling
doi:10.1137/1.9781611970067
Charles A. Micchelli
Mathematical Aspects of Geometric Modeling
20120525T05:37:21Z
10.1137/1.9781611970067
https://epubs.siam.org/doi/book/10.1137/1.9781611970067?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Lectures on Geometric Methods in Mathematical Physics
https://epubs.siam.org/doi/book/10.1137/1.9781611970326?af=R
Lectures on Geometric Methods in Mathematical Physics. <br/> The topics selected for these lectures aim to illustrate some of the ways geometry and analysis can be used in mathematical problems of physical interest. A recurring theme is the role of symmetry, bifurcation and Hamiltonian systems in diverse applications. Despite the old age of these topics and the current explosion of interest and research, the state of knowledge is in my opinion still very primitive. For example, very little is known about dynamical systems that are close to a completely integrable Hamiltonian system. The simplest classical examples, such as the harmonic oscillator, Duffing's equation, the spherical pendulum, the rigid body and the equations of a perfect fluid, show that this program is both interesting and complex. Symmetry is relevant because many examples are, or are close to, a Hamiltonian system which is invariant under some Lie group. Such dynamical systems are very sensitive to perturbations in their equations; or, if you wish, these models are qualitatively unstable. This means that they are bifurcation points in the set of all dynamical systems. The following paragraphs briefly describe how this theme occurs in the various lectures.
Lectures on Geometric Methods in Mathematical Physics. <br/> The topics selected for these lectures aim to illustrate some of the ways geometry and analysis can be used in mathematical problems of physical interest. A recurring theme is the role of symmetry, bifurcation and Hamiltonian systems in diverse applications. Despite the old age of these topics and the current explosion of interest and research, the state of knowledge is in my opinion still very primitive. For example, very little is known about dynamical systems that are close to a completely integrable Hamiltonian system. The simplest classical examples, such as the harmonic oscillator, Duffing's equation, the spherical pendulum, the rigid body and the equations of a perfect fluid, show that this program is both interesting and complex. Symmetry is relevant because many examples are, or are close to, a Hamiltonian system which is invariant under some Lie group. Such dynamical systems are very sensitive to perturbations in their equations; or, if you wish, these models are qualitatively unstable. This means that they are bifurcation points in the set of all dynamical systems. The following paragraphs briefly describe how this theme occurs in the various lectures. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/cb/1981/1.9781611970326/1.9781611970326/production/1.9781611970326.cover.jpg" alttext="cover image"/></p>
Lectures on Geometric Methods in Mathematical Physics
doi:10.1137/1.9781611970326
Jerrold E. Marsden
Lectures on Geometric Methods in Mathematical Physics
20120525T05:31:23Z
10.1137/1.9781611970326
https://epubs.siam.org/doi/book/10.1137/1.9781611970326?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.

Cardinal Spline Interpolation
https://epubs.siam.org/doi/book/10.1137/1.9781611970555?af=R
Cardinal Spline Interpolation. <br/> In the paper [63], written during 1944–45 at the Ballistics Research Laboratories, Aberdeen, Maryland, the author developed certain methods for the smooth approximation of empirical tables. He would have profited greatly from the results of the paper [57] by Quade and Collatz, but heard of its existence only as late as the Fall of 1964. Rather, the paper [63] was strongly suggested by the actuarial work on Osculatory Interpolation so aptly summarized and extended in Greville's paper [33]. In 1944–45 applicable methods were needed, and there was no time to develop their mathematical properties. The present monograph aims at doing that. It is based on a number of papers in our list of references, but mainly on the eight papers [1]–[8]. The opportunity of describing the whole animal in one place, rather than limb by limb, leads to economy; moreover, the assembling of the limbs becomes more functional and biologically viable.
Cardinal Spline Interpolation. <br/> In the paper [63], written during 1944–45 at the Ballistics Research Laboratories, Aberdeen, Maryland, the author developed certain methods for the smooth approximation of empirical tables. He would have profited greatly from the results of the paper [57] by Quade and Collatz, but heard of its existence only as late as the Fall of 1964. Rather, the paper [63] was strongly suggested by the actuarial work on Osculatory Interpolation so aptly summarized and extended in Greville's paper [33]. In 1944–45 applicable methods were needed, and there was no time to develop their mathematical properties. The present monograph aims at doing that. It is based on a number of papers in our list of references, but mainly on the eight papers [1]–[8]. The opportunity of describing the whole animal in one place, rather than limb by limb, leads to economy; moreover, the assembling of the limbs becomes more functional and biologically viable. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/books/content/cb/1973/1.9781611970555/1.9781611970555/production/1.9781611970555.cover.jpg" alttext="cover image"/></p>
Cardinal Spline Interpolation
doi:10.1137/1.9781611970555
I. J. Schoenberg
Cardinal Spline Interpolation
20120525T05:27:22Z
10.1137/1.9781611970555
https://epubs.siam.org/doi/book/10.1137/1.9781611970555?af=R
All rights reserved. Printed in the United States of America. No part of this book may be reproduced, stored, or transmitted in any manner without the written permission of the publisher. For information, write to the Society for Industrial and Applied Mathematics, 3600 Market Street, Philadelphia, PA 191042688.