Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:369

Article

Imakura, Akira¹  Morikuni, Keiichi¹  Takayasu, Akitoshi¹ 

[1] Univ Tsukuba, Fac Engn Informat & Syst, 1-1-1 Tennodai, Tsukuba, Ibaraki 3058573, Japan

关键词: Partial eigenproblem;    Contour integral;    Complex moment;    Verified numerical computations;   

DOI  :  10.1016/j.cam.2019.112543

来源: Elsevier

【 摘 要 】

We propose a verified computation method for partial eigenvalues of a Hermitian generalized eigenproblem. The block Sakurai-Sugiura Hankel method, a contour integral type eigensolver, can reduce a given eigenproblem into a generalized eigenproblem of block Hankel matrices whose entries consist of complex moments. In this study, we evaluate all errors in computing the complex moments. We derive a truncation error bound of the quadrature. Then, we take numerical errors of the quadrature into account and rigorously enclose the entries of the block Hankel matrices. Each quadrature point gives rise to a linear system, and its structure enables us to develop an efficient technique to verify the approximate solution. Numerical experiments show that the proposed method outperforms a standard method and infer that the proposed method is potentially efficient in parallel. (C) 2019 The Author(s). Published by Elsevier B.V.

【 授权许可】

Free