Both Evans et al. and Li et al. have presented preconditioned methods for linear systems to improve the convergence rates of AOR-type iterative schemes. In this paper, we present a new preconditioner. Some comparison theorems on preconditioned iterative methods for solving L-matrix linear systems are presented. Comparison results and a numerical example show that convergence of the precondition...

on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...

on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

In this paper, we study the convergence of the generalized accelerated overrelaxation (GAOR) iterative method. That is an extension of the classical convergence result of the generalized successive overrelaxation (GSOR) iterative method. We proposed some theorems, which they obtain better results than similar works. By some numerical examples we show the goodness of our results. 2006 Elsevier I...

Convergence analysis of a nested iterative scheme proposed by Bank,Welfert and Yserentant (BWY) ([Numer. Math., 666: 645-666, 1990]) for solving saddle point system is presented. It is shown that this scheme converges under weaker conditions: the contraction rate for solving the (1, 1) block matrix is bound by ( √ 5− 1)/2. Similar convergence result is also obtained for a class of inexact Uzawa...

A preconditioned AOR iterative method is proposed with the preconditioner I + S∗ αβ. Some comparison theorems are given when the coefficient matrix of linear system A is an irreducible L−matrix. The convergence rate of AOR iterative method with the preconditioner I + S∗ αβ is faster than the convergence rate with the preconditioner I + Sα by Li et al. Numerical example verifies comparison theor...

In 1891, Weierstrass presented his famous iterative method for finding all the zeros of a polynomial simultaneously. In this paper we establish three new local convergence theorems for the Weierstrass method with a posteriori and a priori error estimates. The main result of the paper generalizes, improves and complements some well known results of Dochev (1962), Kjurkchiev and Markov (1983) and...

113–123] proved that the convergence rate of the preconditioned Gauss–Seidel method for irreducibly diagonally dominant Z-matrices with a preconditioner I + S α is superior to that of the basic iterative method. In this paper, we present a new preconditioner I + K β which is different from the preconditioner given by Kohno et al. and prove the convergence theory about two preconditioned iterati...