Adaptive Preconditioned Variational Methods For Solving Self-Adjoint Partial Differential Equations

The implementation of the Preconditioned Conjugate Gradient method for the solution of large linear systems arising from the discretization of differential operators, requires the pre-determination of only one iteration parameter. The numerical determination of the optimal value of this constant par...

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Bibliographic Details
Published in:International journal of computer mathematics 2003-05, Vol.80 (5), p.615-627
Main Authors: Demetriou, I. C., Evans, D. J.
Format: Article
Language:English
Subjects:
Adaptive Methods
Conjugate Gradient
Preconditioning
Steepest Descent
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Summary:The implementation of the Preconditioned Conjugate Gradient method for the solution of large linear systems arising from the discretization of differential operators, requires the pre-determination of only one iteration parameter. The numerical determination of the optimal value of this constant parameter, involves the spectral bounds of some matrices and can be obtained in O ( N 2 ) sine function evaluations, where 1/ N is the discretization mesh size. It is shown that this parameter can be chosen in a stable manner in O (1) operations per iteration, if it is allowed to vary with the iteration index from information derived from the gradient parameters.
ISSN:0020-7160
1029-0265
DOI:10.1080/0020716021000014213