Convergence Statements for Projection Type Linear Iterative Methods with Relaxations

Abstract

To determine solutions or generalized solutions of the linear operator equation $Ax=b$ linear iterative methods of the form $x_{n+1}=(I–D_n)x_n+D_{n}b$ are considered for which the operators $T_n=I–D_{n}A$ are norm-reducing outside their fixed point set. Conditions are given which guarantee the convergence of the methods and certain properties of the limit elements.