Roundoff error analysis of the double exponential formula-based method for the matrix sign function
Numerical Analysis
2023-12-05 v2 Numerical Analysis
Abstract
In this paper, we perform a roundoff error analysis of an integration-based method for computing the matrix sign function recently proposed by Nakaya and Tanaka. The method expresses the matrix sign function using an integral representation and computes the integral numerically by the double-exponential formula. While the method has large-grain parallelism and works well for well-conditioned matrices, its accuracy deteriorates when the input matrix is ill-conditioned or highly nonnormal. We investigate the reason for this phenomenon by a detailed roundoff error analysis.
Cite
@article{arxiv.2309.17228,
title = {Roundoff error analysis of the double exponential formula-based method for the matrix sign function},
author = {Tomoya Miyashita and Shuhei Kudo and Yusaku Yamamoto},
journal= {arXiv preprint arXiv:2309.17228},
year = {2023}
}
Comments
6 pages, 1 figure