The RKFIT Algorithm for Nonlinear Rational Approximation
Abstract
The RKFIT algorithm outlined in [M. Berljafa and S. Güttel, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 894--916] is a Krylov-based approach for solving nonlinear rational least squares problems. This paper puts RKFIT into a general framework, allowing for its extension to nondiagonal rational approximants and a family of approximants sharing a common denominator. Furthermore, we derive a strategy for the degree reduction of the approximants, as well as methods for their conversion to partial fraction form, for the efficient evaluation, and for root-finding. We also discuss similarities and differences between RKFIT and the popular vector fitting algorithm. A MATLAB implementation of RKFIT is provided, and numerical experiments, including the fitting of a multiple-input/multiple-output (MIMO) dynamical system and an optimization problem related to exponential integration, demonstrate its applicability.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A2049 - A2071
DOI: 10.1137/15M1025426
ISSN (online): 1095-7197
Copyright
© 2017, Society for Industrial and Applied Mathematics. This work is licensed under a Creative Commons Attribution 4.0 International License
History
Submitted: 11 June 2015
Accepted: 10 July 2017
Published online: 19 September 2017
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Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/I01912X/1
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