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SIAM J. on Numerical Analysis

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1967

Volume 4, Issue 4, pp. 483-639


Extension of a Recent Paper by Fox, Henrici and Moler on Eigenvalues of Elliptic Operators

Karl L. E. Nickel

SIAM J. Numer. Anal. 4, pp. 483-488 (6 pages) | Cited 12 times

Online Publication Date: July 14, 2006

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Abstract Unavailable

The Semidiscrete Riemann Function

G. J. Kurowski

SIAM J. Numer. Anal. 4, pp. 489-498 (10 pages)

Online Publication Date: July 14, 2006

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Abstract Unavailable

A Direct Method for Generalized Matrix Inversion

R. P. Tewarson

SIAM J. Numer. Anal. 4, pp. 499-507 (9 pages) | Cited 10 times

Online Publication Date: July 14, 2006

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A method for computing the generalized inverse of a matrix is described. It is especially suited for large sparse matrices. It uses the well-known Gauss-Jordan elimination scheme in conjunction with the conventional Gram-Schmidt orthogonalization process.

Accelerating the Convergence of Discretization Algorithms

Victor Pereyra

SIAM J. Numer. Anal. 4, pp. 508-533 (26 pages) | Cited 15 times

Online Publication Date: July 14, 2006

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Abstract Unavailable

Optimal Quadratures in $L^2 (E_\rho )$. II

Robert E. Barnhill

SIAM J. Numer. Anal. 4, pp. 534-541 (8 pages) | Cited 3 times

Online Publication Date: July 14, 2006

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Abstract Unavailable

Rational Function Approximation As a Well-Conditioned Matrix Eigenvalue Problem

A. Pelios

SIAM J. Numer. Anal. 4, pp. 542-547 (6 pages)

Online Publication Date: July 14, 2006

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A Note on Generalized Interpolation and the Pseudoinverse

Gary P. Herring

SIAM J. Numer. Anal. 4, pp. 548-556 (9 pages) | Cited 3 times

Online Publication Date: July 14, 2006

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Characterization of Chebyshev Approximations by Splines

John R. Rice

SIAM J. Numer. Anal. 4, pp. 557-565 (9 pages) | Cited 8 times

Online Publication Date: July 14, 2006

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Bernstein Polynomials and Monte Carlo Integration

Lloyd Rosenberg

SIAM J. Numer. Anal. 4, pp. 566-574 (9 pages) | Cited 3 times

Online Publication Date: July 14, 2006

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Two variance reducing techniques, the method of control variates and the method of importance sampling, which are used in increasing the efficiency of a Monte Carlo evaluation of an integral, are described. It is shown under very general conditions that the Bernstein polynomials can serve as both a control variate and an importance sampling function. In addition these methods can also be combined to further increase the efficiency of the Monte Carlo evaluation. An example is given to illustrate the method.

Numerical Elliptic Continuation

Richard Saylor

SIAM J. Numer. Anal. 4, pp. 575-581 (7 pages) | Cited 3 times

Online Publication Date: July 14, 2006

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Some Stability Theorems for Ordinary Difference Equations

James Hurt

SIAM J. Numer. Anal. 4, pp. 582-596 (15 pages) | Cited 14 times

Online Publication Date: July 14, 2006

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LaSalle [5], [6], [7] and others have developed a generalization of the “second method” of Liapunov which utilizes certain invariance properties of solutions of ordinary differential equations. Invariance properties of solutions of ordinary difference equations are utilized here to develop stability theorems similar to those in LaSalle [5]. As illustrations of the application of these theorems, a region of convergence is derived for the Newton-Raphson and secant iteration methods. A modification of one of these theorems is given and applied to study the effect of roundoff errors in the Newton-Raphson and Gauss-Seidel iteration methods.

An Analysis of the Numerical Stability of Predictor-Corrector Solutions of Nonlinear Ordinary Differential Equations

Robert J. Lambert

SIAM J. Numer. Anal. 4, pp. 597-606 (10 pages) | Cited 1 time

Online Publication Date: July 14, 2006

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Abstract Unavailable

Some Singular Explicit Fifth Order Runge-Kutta Solutions

H. P. Konen and H. A. Luther

SIAM J. Numer. Anal. 4, pp. 607-619 (13 pages) | Cited 1 time

Online Publication Date: July 14, 2006

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An Order Six Runge-Kutta Process with Extended Region of Stability

J. Douglas Lawson

SIAM J. Numer. Anal. 4, pp. 620-625 (6 pages) | Cited 3 times

Online Publication Date: July 14, 2006

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Discretization and Error Estimates for Elliptic Boundary Value Problems of the Fourth Order

Miloš Zlámal

SIAM J. Numer. Anal. 4, pp. 626-639 (14 pages) | Cited 2 times

Online Publication Date: July 14, 2006

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Abstract Unavailable
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