期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 369, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cam.2019.112546
关键词
Linear system; Verified solution; Error bound; H-matrix
资金
- MEXT as Exploratory Issue on Post-K computer (Development of verified numerical computations and super high-performance computing environment for extreme researches)
- JSPS KAKENHI [17K12692]
- Grants-in-Aid for Scientific Research [17K12692] Funding Source: KAKEN
We derive verified error bounds for approximate solutions of dense linear systems. There are verification methods using an approximate inverse of a coefficient matrix as a preconditioner, where the preconditioned coefficient matrix is likely to be an H-matrix (also known as a generalized diagonally dominant matrix). We focus on two inclusion methods of matrix multiplication for the preconditioning and propose verified error bounds adapted to the inclusion methods. These proposed error bounds are tighter than conventional ones, especially in critically ill-conditioned cases. Numerical results are presented showing the effectiveness of the proposed error bounds. (C) 2019 Elsevier B.V. All rights reserved.
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