Zur Konvergenz von Iterationsverfahren mit affinen Operatoren

Abstract

Many well-known numerical procedures for the iterative solution of linear equations in Banach spaces have the form

x_{n + 1} = A_{n} A_{n - 1} \dots A_{0} x_{0} (n = 0, 1, 2, \dots)

with affine operators $A_{n}$ . If the operators $A_{n}$ possess common fixed points, then there often exist affine projectors $P$ with the property

P = A_{n} P = PA_{n} (n = 0, 1, 2, \dots) .

In this paper some convergence theorems are proved for iteration methods having such operator sequences.

Dieter Schott, Zur Konvergenz von Iterationsverfahren mit affinen Operatoren. Z. Anal. Anwend. 2 (1983), no. 2, pp. 145–157