Fast verified solutions of sparse linear systems with H-matrices

A. Minamihata, K. Sekine, T. Ogita, Shinichi Oishi

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    Abstract

    This paper is concerned with the problem of verifying the accuracy of an approximate solution of a sparse linear system whose coefficient matrix is an H-matrix. Fast and efficient methods of calculating componentwise error bounds of the computed solution are proposed. The methods are based on the verified criterion for an M-matrix. The main point of this article is that the proposed methods can be applied with any iterative solution methods such as the Gauss-Seidel method and Krylov subspace methods. Therefore, the sparsity of the coefficient matrix is preserved in the verification process. Numerical results are presented, illustrating the performance of the proposed methods.

    Original languageEnglish
    Pages (from-to)127-141
    Number of pages15
    JournalReliable Computing
    Volume19
    Issue number2
    Publication statusPublished - 2013

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    Keywords

    • H-matrix
    • Sparse linear systems
    • Verified numerical computations

    ASJC Scopus subject areas

    • Software
    • Applied Mathematics
    • Computational Mathematics

    Cite this

    Minamihata, A., Sekine, K., Ogita, T., & Oishi, S. (2013). Fast verified solutions of sparse linear systems with H-matrices. Reliable Computing, 19(2), 127-141.