Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30174
Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems

Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi

Abstract:

We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.

Keywords: rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1082973

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1434

References:


[1] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia 1994.
[2] R. E. Cline, Inverses of rank invariant powers of a matrix, SIAM J. Numer. Anal. 5 (1968) 182-197.
[3] A. Hadjidimos, Accelerated overrelaxation method, Math. Comput. 32 (1978) 149-157.
[4] Y. Huang and Y. Song, AOR iterative methods for rank deficient least squares problems, J. Appl. Math. Comput. 26 (2008) 105-124.
[5] V. A. Miller and M. Neumann, Successive overrelaxation methods for solving the rank deficient linear squares problem, Linear Algebra Appl 88/89 (1987) 533-557.
[6] H. Tian, Accelerate overrelaxation methods for rank deficient linear systems, Appl. Math. Comput. 140 (2003) 485-499.