Preconditioned Conjugate Gradient Methods for Integral Equations of the Second Kind Defined on the Half-Line
Year: 1996
Journal of Computational Mathematics, Vol. 14 (1996), Iss. 3 : pp. 223–236
Abstract
We consider solving integral equations of the second kind defined on the half-line $[0,\infty)$ by the preconditioned conjugate gradient method. Convergence is known to be slow due to the non-compactness of the associated integral operator. In this paper, we construct two different circulant integral operators to be used as preconditioners for the method to speed up its convergence rate. We prove that if the given integral operator is close to a convolution-type integral operator, then the preconditioned systems will have spectrum clustered around 1 and hence the preconditioned conjugate gradient method will converge superlinearly. Numerical examples are given to illustrate the fast convergence.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1996-JCM-9233
Journal of Computational Mathematics, Vol. 14 (1996), Iss. 3 : pp. 223–236
Published online: 1996-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14