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.
A PRECONDITIONING MATRIX FOR THE CHEBYSHEV DIFFERENCING OPERATOR / Funaro, Daniele. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 24:(1987), pp. 1024-1031. [10.1137/0724067]
A PRECONDITIONING MATRIX FOR THE CHEBYSHEV DIFFERENCING OPERATOR
FUNARO, Daniele
1987
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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