|Table of Contents|

Optimal AOR for Rank Deficient Least Squares Problem(PDF)

《南京师大学报(自然科学版)》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2011年04期
Page:
1-8
Research Field:
数学
Publishing date:

Info

Title:
Optimal AOR for Rank Deficient Least Squares Problem
Author(s):
Tan Xueyuan
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210046,China
Keywords:
AOR methodsoptimal parameters2-cyclicasymptotical semiconvergence factorrank deficient linear least squares problem
PACS:
O241.6
DOI:
-
Abstract:
This paper studied the optimal parameters and asymptotical semiconvergence factor of AOR methods for rank deficient linear least squares problem and presented the explicit expressions of these factors. Finally,two numerical examples are given to illustrate our results.

References:

[1] Chen Y T. Iterative methods for linear squares problems[D]. Ontario: University of Waterloo,1975.
[2] Niethammer W,J de Pillis,Varga R S. Convergence of block iterative methods applied to sparse least squares problems[J]. Linear Algebra Appl,1984, 58: 327-324.
[3] Markham T L,Neumann M,Plemmons R J. Convergence of a direct-iterative method for large-scale least squares problems [J]. Linear Algebra Appl,1985, 69: 155-167.
[4] Saridakis Y G. An algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problems [J]. J Comput Appl Math,1988, 24: 209-225.
[5] Miller V A,Neumann M. Successive overrelaxation methods for solving the rank deficient least squares problem[J]. Linear Algebra Appl, 1987, 88 /89: 533-557.
[6] Tian Hongjun. Accelarated overrelaxation methods for rank deficient linear systems[J]. Appl Math Comput,2003, 140: 485- 499.
[7] Tan Xueyuan,Song Yongzhong. Optimal parameters for 2-cyclic AOR[J]. Appl Math Comput,2010, 216: 1 428-1 442.
[8] Varga R S. Matrix Iterative Analysis[M]. 2nd ed. Berlin: Springer-Verlag,2000.
[9] Hadjidimos A. Successive overrelaxation and related methods[J]. J Comput Appl Math,2000, 123: 177-199.
[10] Sisler M. Uber ein Zweiparametrigen Iterationsverfahrens[J]. Apl Mat, 1973( 18) : 325-332.

Memo

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Last Update: 2013-03-21