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arXiv · 2003.06410

Algorithms for the rational approximation of matrix-valued functions

Ion Victor Gosea·Stefan Güttel
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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.

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Ion Victor Gosea, Stefan Güttel. 2020-03-13. Algorithms for the rational approximation of matrix-valued functions. https://arxiv.org/abs/2003.06410

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