Algorithms for the rational approximation of matrix-valued functions

Gosea, Ion Victor and Güttel, Stefan (2021) Algorithms for the rational approximation of matrix-valued functions. [MIMS Preprint]

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Abstract

A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method based on low-rank approximation of a block Loewner matrix. A new method, called the block-AAA algorithm, based on a generalized barycentric formula with matrix-valued weights is proposed. All algorithms are compared in terms of obtained approximation accuracy and runtime on a set of problems from model order reduction and nonlinear eigenvalue problems, including examples with noisy data. It is found that interpolation-based methods are typically cheaper to run, but they may suffer in the presence of noise for which approximation-based methods perform better.

Item Type: MIMS Preprint
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Stefan Güttel
Date Deposited: 22 Apr 2021 08:41
Last Modified: 22 Apr 2021 08:41
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2809

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