A Preconditioning Matrix for the Chebyshev Differencing Operator
Abstract
An efficient preconditioner for the Chebyshev differencing operator is considered. The corresponding preconditioned eigenvalues are real and positive and lie between 1 and ${\pi / 2}$. An eixpelicit formula for these eigenvalues and the corresponding eigenfunctions is given. The results are generalized to the case of operators related to Chebyshev discretizations of systems of linear differential equations.
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Copyright © 1987 Society for Industrial and Applied Mathematics.
History
Submitted: 3 March 1986
Accepted: 1 October 1986
Published online: 14 July 2006
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