Convergence theorems for block splitting iterative methods for linear systems

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...

Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems

Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...

Convergence Theorems for Two Iterative Methods A stationary iterative method for solving the linear system:

Recasting this in the form above we have 1 B M N − = − and . 1 c M b − = It is easy to show that this iteration is consistent for any splitting as long as M is nonsingular. Obviously, to be practical the matrix M must be selected so that the system My d = is easily solved. Popular choices for M are diagonal matrices (as in the Jacobi method), lower triangular matrices (as in the Gauss-Seidel an...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Convergence of nested classical iterative methods for linear systems

Classical iterative methods for the solution of algebraic linear systems of equations proceed by solving at each step a simpler system of equations. When this system is itself solved by an (inner) iterative method, the global method is called a two-stage iterative method. If this process is repeated, then the resulting method is called a nested iterative method. We study the convergence of such...