Hisashi Kotakemori

TL;DR: This paper uses the preconditioning matrix I + S(α) to show that if a coefficient matrix A is an irreducibly diagonally dominant Z-matrix, then [I + S (α)]A is also a strictly diagonal dominant Z -matrix and is shown that the proposed method is also superior to other iterative methods.

TL;DR: In this paper, the modified Gauss-Seidel method with a preconditioner (I + Smax) instead of (I+S) was proposed, where Smax is constructed by only the largest element at each row of the upper triangular part of A. By using the lemma established Neumann and Plemmons (Linear Algebra Appl. 88/89 (1987) 559), they get the comparison theorem for the proposed method.

TL;DR: This paper generalizes the preconditioner to the type (I + @bU), where @b is a positive real number, and proposes an algorithm for estimating the optimum @b.

TL;DR: A preconditioned iterative method for solving the linear system Ax = b is considered, which is a generalization of a method proposed in Kotakemori et al.

TL;DR: In this article, the convergence analysis for modified Gauss-Seidel and Jacobi type iterative methods is presented and a comparison of spectral radius among the Gauss -Seidel iterative method and these modified methods is provided.

TL;DR: The present work is a contribution towards the generalization of the most common preconditioners for linear systems whose matrix coefficient is an M-matrix.

TL;DR: An iterative method based on the Block Gauss–Seidel method is employed to determine the steady state probabilities of a general repairable k-out-of-n:G system with non-identical components, which is a common form of redundancy.

TL;DR: Comparisons between some splittings for preconditioned matrices used for improving the convergence rate of the Gauss-Seidel method are derived on the basis of nonnegative matrix.

TL;DR: The convergence and comparison theorems of newly proposed splitting method with two preconditioner are given and a new splitting method for tensors is proposed.