Roundoff error analysis of the double exponential formula-based method for the matrix sign function

Autor:	Miyashita, Tomoya, Kudo, Shuhei, Yamamoto, Yusaku
Rok vydání:	2023
Předmět:	Mathematics - Numerical Analysis 65D30 65F30 65G50 G.1.3 G.1.4
Druh dokumentu:	Working Paper
Popis:	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. Comment: 6 pages, 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.17228 Zobrazit plný text záznamu View this record from Arxiv