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ALGORITHMS FOR THE RATIONAL APPROXIMATION OF MATRIX-VALUED FUNCTIONS.
- Source :
-
SIAM Journal on Scientific Computing . 2021, Vol. 43 Issue 5, pA3033-A3054. 22p. - Publication Year :
- 2021
-
Abstract
- A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory adaptive Antoulas--Anderson (AAA) method, the rational Krylov fitting (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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *APPROXIMATION algorithms
*ALGORITHMS
*NONLINEAR equations
*KRYLOV subspace
Subjects
Details
- Language :
- English
- ISSN :
- 10648275
- Volume :
- 43
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Scientific Computing
- Publication Type :
- Academic Journal
- Accession number :
- 153519525
- Full Text :
- https://doi.org/10.1137/20M1324727