Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems
نویسندگان
چکیده
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 iterative method, Gauss-Seidel iterative method, semiconvergence.
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