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

Author:

Miyashita Tomoya1,Kudo Shuhei1,Yamamoto Yusaku1

Affiliation:

1. School of Informatics and Engineering, The University of Electro-Communications

Publisher

The Japan Society for Industrial and Applied Mathematics

Reference7 articles.

1. [1] N. J. Higham, Functions of Matrices: Theory and Computation, SIAM, Philadelphia, 2008.

2. [2] Y. Nakatsukasa and N. J. Higham, Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD, SIAM J. Sci. Comput., 35 (2013), A1325–A1349.

3. [3] T. Nakaya and K. Tanaka, Numerical computation of matrix sign function by double exponential formula (in Japanese), Trans. JSIAM, 31 (2021), 105–132.

4. [4] H. Takahasi and M. Mori, Double exponential formulas for numerical integration, Publ. RIMS Kyoto Univ., 9 (1974), 721–741.

5. [5] T. Miyashita and Y. Yamamoto, Improvement and application of the double exponential formula-based computation method for the matrix sign function (in Japanese), in: Proc. of 2022 Annual Meeting of JSIAM, No. C1-3-2, The Japan Society for Industrial and Applied Mathematics, 2022.

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