Journal of Soviet Mathematics

, Volume 28, Issue 3, pp 397–402 | Cite as

Generalized method of conjugate gradients for the solution of linear systems

  • G. V. Savinov


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.


Linear System Finite Number Algebraic Equation Conjugate Gradient Convergence Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 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. 2.
    O. Axelsson, “A generalized SSOR method,” B.I.T.,12, No. 4, 443–467 (1972).Google Scholar
  3. 3.
    G. V. Savinov, “The construction of multistep relaxation methods,” Tr. Leningr. Korablestroit. Inst.,97, 114–119 (1975).Google Scholar
  4. 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. 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

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • G. V. Savinov

There are no affiliations available

Personalised recommendations