JournalszaaVol. 2, No. 2pp. 145–157

Zur Konvergenz von Iterationsverfahren mit affinen Operatoren

  • Dieter Schott

    Hochschule Wismar, Germany
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Abstract

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

xn+1=AnAn1A0x0(n=0,1,2,)x_{n+1} = \mathbf A_n \mathbf A_{n-1} \dots \mathbf A_0x_0 (n = 0, 1, 2, \dots)

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

P=AnP=PAn(n=0,1,2,).\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.

Cite this article

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

DOI 10.4171/ZAA/56