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EIGENVALUES FOR THE SEMI-CIRCULANT PRECONDITIONING OF ELLIPTIC OPERATORS WITH THE VARIABLE COEFFICIENTS
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 Title & Authors
EIGENVALUES FOR THE SEMI-CIRCULANT PRECONDITIONING OF ELLIPTIC OPERATORS WITH THE VARIABLE COEFFICIENTS
Kim, Hoi-Sub; Kim, Sang-Dong; Lee, Yong-Hun;
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 Abstract
We investigate the eigenvalues of the semi-circulant preconditioned matrix for the finite difference scheme corresponding to the second-order elliptic operator with the variable coefficients given by , where a and b are continuously differentiable functions and d is a positive bounded function. The semi-circulant preconditioning operator is constructed by using the leading term of plus the constant reaction term such that . Using the field of values arguments, we show that the eigenvalues of the preconditioned matrix are clustered at some number. Some numerical evidences are also provided.
 Keywords
semi-circulant preconditioning;central finite difference;field of values;
 Language
English
 Cited by
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