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Mathematics of Computation

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A mesh refinement method for $ Ax=\lambda Bx$

Author: Stephen F. McCormick
Journal: Math. Comp. 36 (1981), 485-498
MSC: Primary 65N25; Secondary 65F15, 65L15, 65R99
MathSciNet review: 606508
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Abstract: The aim of this paper is to introduce a simple but efficient mesh refinement strategy for use with inverse iteration for finding one or a few solutions of an ordinary or partial differential eigenproblem of the form $ Ax = \lambda Bx$. The focus is upon the case where A and B are symmetric and B is positive definite, although the approaches have a very broad application. A discussion of the combined use of mesh refinement and a correction scheme multigrid technique is also provided. The methods are illustrated by numerical results from experiments with two-point boundary value problems.

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Article copyright: © Copyright 1981 American Mathematical Society

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