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SIAM J. on Numerical Analysis / Volume 23 / Issue 4

SIAM J. Numer. Anal. 23, pp. 717-733 (17 pages)

On the Successive Projections Approach to Least-Squares Problems

J. E. Dennis, Jr. and Trond Steihaug

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In this paper, we suggest a generalized Gauss–Seidel approach to sparse linear and nonlinear least-squares problems. The algorithm, closely related to one given by Elfving (1980), uses the work of Curtis, Powell, and Reid (1974) as extended by Coleman and Moré (1983) to divide the variables into nondisjoint groups of structurally orthogonal columns and then projects the updated residual into each column subspace of the Jacobian in turn. In the linear case, this procedure can be viewed as an alternate ordering of the variables in the Gauss–Seidel method. Preliminary tests indicate that this leads quickly to cheap solutions of limited accuracy for linear problems, and that this approach is promising for an inexact Gauss–Newton analog of the inexact Newton approach of Dembo, Eisenstat, and Steihaug (1982).

© 1986 Society for Industrial and Applied Mathematics

KEYWORDS

AMS Subject Headings

65F10, 32-04

PUBLICATION DATA

ISSN

0036-1429 (print)  
1095-7170 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received October 11, 1983
Digital Object Identifier
http://dx.doi.org/10.1137/0723047

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