Gauss-Seidel Iterative Methods for Rank Deficient Least Squares Problems

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.

Authors:

• Davod Khojasteh Salkuyeh
• Sayyed Hasan Azizi

Keywords:

• rank deficient least squares problems
• AOR iterativemethod
• Gauss-Seidel iterative method
• semiconvergence.

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