Hideo Sawami

An iterative test for H -matrix

Abstract For many applications it is very useful to know whether a matrix is an H -matrix or not. Harada et al. proposed simple algorithm which is produced iteratively a positive diagonal matrix D in Bishan Li et al. (Linear Algebra Appl. 271 (1998) 179–190). This method is useful when matrix A is an H -matrix, and when A is not an H -matrix, a wasteful computation is necessary. In this paper, to conquer this drawback, we propose a new algorithm.

The Gauss-Seidel iterative method with the preconditioning matrix (I +S +Sm)

We propose a preconditioned iterative method with the preconditioning matrixPsm =I +S +Sm forAx =b, whereA is an irreducibly diagonal dominantZ-matrix with unit diagonal. The convergence property and the comparison theorem of the proposed method are discussed. Moreover, some numerical examples are reported to confirm the theoretical analysis.

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).

Arbitrarily Shaped Hollow Waveguide Analysis by the

An efficient numerical method named the

\alpha

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-Interpolation Method

-interpolation method (AIM) has been developed for solving hollow waveguide problems. The AIM is a simpler and more systematic procedure than the finite-element method. And when the optimum interpolation parameter is chosen for any number of linear triangular elements, the cutoff wavenumbers or the exact eigenvalues may be estimated by the AIM. Numerical results and comparisons are given.

On the accelerated iterative method for estimating the optimum overrelaxation parameter

Abstract This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.

Note on the non-stationary iterative method for the estimation of the optimum overrelaxation parameter

Abstract We study the cause for the overestimation of the optimum overrelaxation factor when a non-stationary iterative method of Carres or Kulsuds type is used. In addition we show that when the overrelaxation factor is substantially changed the estimation process becomes more difficult. The overestimation phenomena are also shown numerically.

An Iterative Method Applied to Nonsymmetric Linear Systems

For solving the matrix equation Ax=b, with coefficient matrix being the identity plus the skew-symmetric part ofA, a variety of extrapolated iterative methods are reported. These methods using an optimum extrapolation parameter are able to give a better asymptotic convergence rate. In this paper we propose an, iterative method without the parameter estimation.

On iterative methods for solving a semi-linear eigenvalue problem

For the semi-linear eigenvalue problem of the form Ax = lF{x), where F is a nonlinear map-ping, we present some methods for numerical solution. For this problem, we first describe a practical SOR method: in this method, the overrelaxation parameter automatically estimated is used instead of the optimum value, since the eigenvalue is not known a priori. We discuss the convergence of this Newton-like method. We then present a conjugate gradient (CG) method for the eigenvalue problem. We also discuss some preconditioning techniques for the present CG method. Finally, a comparison of the convergence rates for these methods is made with a numerical example.