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New results on the convergence of the conjugate gradient method

✍ Scribed by R. Bouyouli; G. Meurant; L. Smoch; H. Sadok

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
120 KB
Volume
16
Category
Article
ISSN
1070-5325

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✦ Synopsis

Abstract

This paper is concerned with proving theoretical results related to the convergence of the conjugate gradient (CG) method for solving positive definite symmetric linear systems. Considering the inverse of the projection of the inverse of the matrix, new relations for ratios of the A‐norm of the error and the norm of the residual are provided, starting from some earlier results of Sadok (Numer. Algorithms 2005; 40:201–216). The proofs of our results rely on the well‐known correspondence between the CG method and the Lanczos algorithm. Copyright Β© 2008 John Wiley & Sons, Ltd.

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