The Davidson Method (Crouzeix et al.)

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SIAM Journal on Scientific Computing
Volume 15-1, January 1994, pp.  62-76
(C) 1994 by Society for Industrial and Applied Mathematics
All rights reserved


Title:            The Davidson Method

Author:           M. Crouzeix, B. Philippe, M. Sadkane

AMS Subject
Classifications:  65F15

Key words:        Davidson method, Lanczos method, Krylov space, 
                  preconditioner, eigenvalue, sparse matrices, 
                  eigenvectors

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ABSTRACT

This paper deals with the Davidson method that computes a few of the 
extreme eigenvalues of a symmetric matrix and corresponding 
eigenvectors.  A general convergence result for methods based on 
projection techniques is given and can be applied to the Lanczos 
method as well. The efficiency of the preconditioner involved in the 
method is discussed. Finally, by means of numerical experiments, the 
Lanczos and Davidson methods are compared and a procedure for a 
dynamic restarting process is described.


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