On the Error Computation for Polynomial Based Iteration Methods

  • Bernd Fischer
  • Gene H. Golub
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 60)


In this note we investigate the Chebyshev iteration and the conjugate gradient method applied to the system of linear equations Ax = f where A is a symmetric, positive definite matrix. For both methods we present algorithms which approximate during the iteration process the kth error ε k = ||xx k || A . The algorithms are based on the theory of modified moments and Gaussian quadrature. The proposed schemes are also applicable for other polynomial iteration schemes. Several examples, illustrating the performance of the described methods, are presented.


Orthogonal Polynomial Conjugate Gradient Method Continue Fraction Positive Definite Matrix Initial Error 
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Copyright information

© Springer-Verlag New York, Inc 1994

Authors and Affiliations

  • Bernd Fischer
    • 1
  • Gene H. Golub
    • 2
  1. 1.Institute of Applied MathematicsUniversity of HamburgHamburgGermany
  2. 2.Department of Computer ScienceStanford UniversityStanfordUSA

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