Solutions toH-systems by topological and iterative methods

Solutions to H-systems by Topological and Iterative Methods

Richardson and Chebyshev Iterative Methods by Using G-frames

In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern,  Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper...

On the modified iterative methods for $M$-matrix linear systems

This paper deals with scrutinizing the convergence properties of iterative methods to solve linear system of equations. Recently, several types of the preconditioners have been applied for ameliorating the rate of convergence of the Accelerated Overrelaxation (AOR) method. In this paper, we study the applicability of a general class of the preconditioned iterative methods under certain conditio...

Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods

In stationary iterative methods for solving linear systems Ax = b, the iteration x = Hx + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x. We present a theorem which yields componentwise error estimates for x, and clarify the relation between our result and a previous result.

On General Iterative Methods for the Solutions

1. Introduction. General iterative methods based on the notions of the relative error functional and the projection are introduced for the solutions of a class of nonlinear operator equations in Hilbert space. It is shown that general iterative procedures based on the variational theory of operators (which include the classical steepest descent method and other gradient methods) are first-order...