Abstract: Several previous papers have given an analysis of the convergence of a variational solution of an inhomogeneous operator equation under a basic assumption (that of asymptotic diagonality of type A, B, C) as to the structure of the operator matrix. We seek here to weaken the assumptions made as much as is consistent with this method of analysis, and use the concepts of strongly and weakly asymptotically diagonal systems introduced in Delves & Musa (1976). The systems covered in the previous analysis are also strongly A.D.; all strongly A.D. systems are weakly A.D.; and we give a complete convergence analysis for weakly A.D. systems which reduces in all essential aspects to the previous one in the appropriate special cases. The results obtained here have the following advantages over the classical approach: (1) Explicit estimates of the rates of convergence are obtained. (2) These estimates use only quantities computed during the course of a calculation; they are therefore easy and cheap to use in practice. (3) It is not assumed that the operator involved is positive definite.
Publication Year: 1979
Publication Date: 1979-01-01
Language: en
Type: article
Indexed In: ['crossref']
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