Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices

This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of band...

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Bibliographic Details
Published in:BIT 2019-12, Vol.59 (4), p.969-986
Main Authors: Pozza, Stefano, Simoncini, Valeria
Format: Article
Language:English
Subjects:
Approximation
Computational Mathematics and Numerical Analysis
Decay
Iterative methods
Mathematical analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Polynomials
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Summary:This paper derives a priori residual-type bounds for the Arnoldi approximation of a matrix function together with a strategy for setting the iteration accuracies in the inexact Arnoldi approximation of matrix functions. Such results are based on the decay behavior of the entries of functions of banded matrices. Specifically, a priori decay bounds for the entries of functions of banded non-Hermitian matrices will be exploited, using Faber polynomial approximation. Numerical experiments illustrate the quality of the results.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-019-00763-6