The RKFIT algorithm for nonlinear rational approximation

Berljafa, Mario and Güttel, Stefan (2015) The RKFIT algorithm for nonlinear rational approximation. [MIMS Preprint]

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Abstract

The RKFIT algorithm outlined in [M. Berljafa and S. Güttel, Generalized rational Krylov decompositions with an application to rational approximation, SIAM J. Matrix Anal. Appl., 2015] 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 root-finding. We also discuss commons and differences of RKFIT and the popular vector fitting algorithm. A MATLAB implementation of RKFIT is provided and numerical experiments, including the fitting of a MIMO dynamical system and an optimization problem related to exponential integration, demonstrate its applicability.

Item Type: MIMS Preprint
Uncontrolled Keywords: nonlinear rational approximation, least squares, rational Krylov method
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 41 Approximations and expansions
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 10 Jun 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2309

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