Generalized method of conjugate gradients for the solution of linear systems
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We obtain convergence criteria for the generalized method of conjugate gradients for solving systems of linear algebraic equations; they imply the convergence of the method in a finite number of steps. The theorem proved in the paper allows at the same time to consider the known variants of the generalized method of conjugate gradients, as well as to devise new modifications for the convergence of this method.
KeywordsLinear System Finite Number Algebraic Equation Conjugate Gradient Convergence Criterion
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- 1.G. I. Marchuk and Yu. A. Kuznetsov, “Iteration methods and quadratic functionals,” in: Methods of Computational Mathematics [in Russian], Nauka, Novosibirsk (1975), pp. 4–143.Google Scholar
- 2.O. Axelsson, “A generalized SSOR method,” B.I.T.,12, No. 4, 443–467 (1972).Google Scholar
- 3.G. V. Savinov, “The construction of multistep relaxation methods,” Tr. Leningr. Korablestroit. Inst.,97, 114–119 (1975).Google Scholar
- 4.M. R. Hestenes and E. Stiefel, “Method of conjugate gradients for solving linear systems,” J. Res. Nat. Bur. Stand.,49, 409 (1952).Google Scholar
- 5.P. Concus and G. H. Golub, “A generalized conjugate gradient method for nonsymmetric systems of linear equations,” Lect. Notes Econ. Math. Systems,134, 56–65 (1976).Google Scholar