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

$$
x_{n+1} = \mathbf A_n \mathbf A_{n-1} \dots \mathbf A_0x_0 (n = 0, 1, 2, \dots)
$$

with affine operators $\mathbf A_n$. If the operators $\mathbf A_n$ possess common fixed points, then there often exist affine projectors $\mathbf P$ with the property

$$
\mathbf P = \mathbf A_n \mathbf P = \mathbf {PA}_n \quad (n= 0, 1,2, \dots).
$$

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

Zur Konvergenz von Iterationsverfahren mit affinen Operatoren

Dieter Schott

Abstract

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