Iteration number for the conjugate gradient method

Mathematics and Computers in Simulation

Volumn 61, Issue 3-6, 2003, Pages 421-435

  Axelsson, Owe ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Conjugate gradient method; Eigenvalues; Iteration number

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LINEAR SYSTEMS; PROBLEM SOLVING;

CONJUGATE GRADIENT METHODS;

GRADIENT METHODS;

EID: 0037472514     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(02)00097-6     Document Type: Conference Paper

References (8)

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2. O. Axelsson, On the rate of convergence of the conjugate gradient method, in: Jiang Er-Xiong (Ed.), Proceedings of the 1992 Conference on Shanghai International Numerical Algebra and Its Applications, China Science and Technology Press, 1993, pp. 13-32.
3. O. Axelsson, Iterative Solution Methods, Cambridge University Press, New York, 1994.
4. O. Axelsson, in: S. Margenov, P.S. Vassilevski (Eds.), Condition Numbers for the Study of the Rate of Convergence of the Conjugate Gradient Method, Iterative Methods in Linear Algebra II, IMACS, NJ, 1996, pp. 3-33.
5. Greenbaum A., Strakos Z., Predicting the behaviour of finite precision Lanczos and conjugate gradient computations. SIAM J. Matrix Anal. Appl. 13:1992;121-137.
6. Kaporin I.E., New convergence results and preconditioning strategies for the conjugate gradient method. Num. Lin. Alg. Appl. 1:1994;179-210.
7. Notay Y., On the convergence rate of the conjugate gradients in presence of rounding errors. Num. Math. 65:1993;301-317.
8. Padiy A., Axelsson O., Polman B., Generalised augmented matrix preconditioning approach and its application to iterative solution of ill-conditioned algebraic systems. SIAM J. Matrix Anal. Appl. 22:2001;793-818.