Naotaka Okamoto

Accelerated iterative method for Z-matrices

It has recently been reported that the convergence of the preconditioned Gauss-Seidel method which uses a matrix of the type (I + U) as a preconditioner is faster than the basic iterative method. In this paper, we generalize the preconditioner to the type (I + @bU), where @b is a positive real number. After discussing convergence of the method applied to Z-matrices, we propose an algorithm for estimating the optimum @b. Numerical examples are also given, which show the effectiveness of our algorithm.

The alpha interpolation method for the solution of an eigenvalue problem

Abstract We present a weighted residual finite element method for the solution of an eigenvalue problem. As a test function, we take a linear combination of two functions which belong to different spaces. We call this method the alpha interpolation method (AIM) for the eigenvalue problem. We compare the AIM with the Standard-Galerkin finite element method (SGFEM).

Convergence of a preconditioned iterative method for H-matrices

Abstract In this paper, we consider a preconditioned iterative method for solving the linear system Ax = b , which is a generalization of a method proposed in Kotakemori et al. [3] and prove its convergence for the case when A is an H-matrix.

Preconditioned Iterative Methods for Linear Equations Arising from the Boundary Element Method

A precondition for the Gauss–Seidel iterative method to solve a linear system of equations arising from the boundary element method for the Laplace and convective diffusion with first-order reaction problems is presented in this paper. The present precondition is based on the elementary matrix operation. We discuss the effect of the precondition in comparison with the Gauss elimination (GE) method in some numerical experiments.

A Two-step Preconditioning Method for Solving Dense Linear Systems

In this paper, we propose a two-step preconditioning method combined with the preconditioning matrices and In order to decrease the arithmetic operations, we describe a computational procedure. Numerical examples are also given, which show the effectiveness of our algorithm.

An attempt at numerical calculation of natural convection using preconditioned iterative methods

Preconditioning can change the degree of diagonal dominance and the eigenvalue of a coefficient matrix in the solution of a linear system of equations. Accordingly, an appropriate preconditioner can reduce the number of iterations, and further this may also reduce the number of arithmetic operations compared with those by the classical iterative methods without preconditioning. Consider the following preconditioned linear system of equations:

A generalization of the adaptive gauss-seidel method for Z-matrices

We proposed an accelerated Adaptive Gauss-Seidel method with the type (I+βU) as preconditioner in [3]. In this paper we generalize this method and prove a convergence theorem. We show some numerical examples.