Lecture 20

  • Eugene E. Tyrtyshnikov


Consider the expansion of the initial residual \( r_0 = \sum\limits_{i = 1}^k {\xi _i z_i } \) in an orthonormal eigenvector system of the given n × n matrix A = A* > 0.


Conjugate Gradient Method Chebyshev Polynomial Hermitian Matrice Projective Restriction Lanczos Method 
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  1. 1.
    O. Axelsson and G. Lindskog. The rate of convergence of the conjugate gradient method. Numer. Math. 48: 499–523 (1986).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    A. van der Sluis and H.A. van der Vorst. The rate of convergence of conjugate gradients. Numer. Math. 48: 543–560 (1986).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Eugene E. Tyrtyshnikov
    • 1
  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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