Preconditioned sor methods for generalized least-squares problems |
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Authors: | Yuan Jinyun Alfredo N Iusem |
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Institution: | (1) Departmento de Matemática, Universidade Federal do Paraná, Centro Politécnico, CP: 19.081, 81531-990 Curitiba, Brazil;(2) Instituto de Matemática Pura e Aplicada, 22460-320 Rio de Janeiro, RJ, Brazil |
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Abstract: | We consider here iterative methods for the generalized least squares problem defined as min(Ax-b)TW-1 (Ax-b) with W symmetric and positive definite. We develop preconditioned SOR methods specially devised also for the augmented systems of the problem. We establish the convergence region for the relaxation parameter and discuss, for one of the resulting SOR methods, the optimal value of this parameter. The convergence analysis and numerical experiments show that the preconditioned block SOR methods are very good alternatives for solving the problem. |
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Keywords: | cyclic SOR method generalized SOR method least-squares problems generalized least-squares problems convergence optimal parameter |
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