Fast Verified Solutions of Sparse Linear Systems with H-matrices

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 ∗Submitted: February 25, 2013; Revised: September 23, 2013; Accepted: December 5, 2013.