摘要:

An algorithm for the computation of a best monotoneLpapproximate 1≤p<∞ is presented and its convergence theorems are established.

ISSN:0163-0563    

DOI:10.1080/01630569008816403

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

The aim of this paper is to describe some relations between the convergence speed of successive approximations to solutions of linear operator equations, on the one hand, and various spectral properties of the corresponding operators, on the other. We shall show, in particular, that the estimates for the convergence speed of successive approximations is basically determined by certain properties of the pheripheral spectrum of the operator involved (recall that the peripheral spectrum is that part of the spectrum which lies on the boundary, i.e. consists of numbers with absolute values equal to the spectral radius). Equivalently, the convergence speed is characterized by the growth of the (Fredholm) resolvent when approaching the peripheral spectrum. Interestingly, these properties are essentially different for Volterra and non-Volterra operators, where by Volterra operator we mean, as usual, an operator whose spectrum consists only of zero.

ISSN:0163-0563    

DOI:10.1080/01630569008816404

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569008816392

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor