ON DIAGONALLY RELAXED ORTHOGONAL PROJECTION METHODS

被引：104

作者：

Censor, Yair ^{[1
]}

Elfving, Tommy ^{[2
]}

Herman, Gabor T. ^{[3
]}

Nikazad, Touraj ^{[2
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[2] Linkoping Univ, Dept Math, SE-58183 Linkoping, Sweden

[3] CUNY, Grad Ctr, Dept Comp Sci, New York, NY 10016 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2008年 / 30卷 / 01期

基金：

以色列科学基金会; 美国国家卫生研究院;

关键词：

block iteration; convex feasibility; diagonal relaxation; projection methods; simultaneous algorithms;

D O I：

10.1137/050639399

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We propose and study a block-iterative projection method for solving linear equations and/or inequalities. The method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonally relaxed orthogonal projections (DROP). Diagonal relaxation has proven useful in accelerating the initial convergence of simultaneous and block-iterative projection algorithms, but until now it was available only in conjunction with generalized oblique projections in which there is a special relation between the weighting and the oblique projections. DROP has been used by practitioners, and in this paper a contribution to its convergence theory is provided. The mathematical analysis is complemented by some experiments in image reconstruction from projections which illustrate the performance of DROP.

引用

页码：473 / 504

页数：32

共 37 条

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BLOCK-ITERATIVE PROJECTION METHODS FOR PARALLEL COMPUTATION OF SOLUTIONS TO CONVEX FEASIBILITY PROBLEMS [J].