{
"title": "Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems",
"authors": "Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi",
"country": null,
"institution": null,
"volume": "55",
"journal": "International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering",
"pagesStart": 1010,
"pagesEnd": 1015,
"ISSN": "1307-6892",
"URL": "http:\/\/waset.org\/publications\/14436",
"abstract": "We study the semiconvergence of Gauss-Seidel iterative\r\nmethods for the least squares solution of minimal norm of rank\r\ndeficient linear systems of equations. Necessary and sufficient conditions\r\nfor the semiconvergence of the Gauss-Seidel iterative method\r\nare given. We also show that if the linear system of equations is\r\nconsistent, then the proposed methods with a zero vector as an initial\r\nguess converge in one iteration. Some numerical results are given to\r\nillustrate the theoretical results.",
"references": null,
"publisher": "World Academy of Science, Engineering and Technology",
"index": "International Science Index 55, 2011"
}