Hybrid Methods for Solving Systems of Equations
نویسنده
چکیده
The aim of this paper is to review the most important results on the hybrid procedures 7] for solving systems of linear equations. Starting from two iterative methods for solving a system of linear equations, the hybrid procedure consists of constructing a new sequence of iterates with better convergence properties. For a more complete treatment, see 4]. Hybrid procedures were extended to systems of nonlinear equations in 5] and multilevel extensions were studied in 6]. 1 The hybrid procedure Let us consider the p p system of linear equations Ax = b. The hybrid procedure consists of combining the iterates produced by two methods for obtaining a new sequence of iterates with better convergence properties. Let (x 0 n) and (x 00 n) be the sequences given by the two iterative methods. We shall construct a new sequence of iterates (x n) by
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