Fast verified solutions of sparse linear systems with H-matrices

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

研究成果: Article査読

1 被引用数 (Scopus)


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.

ジャーナルReliable Computing
出版ステータスPublished - 2013 12 1

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics

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