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Asymptotic Properties of Collocation Matrix Norms 1: Global Polynomial Approximation

Lookup NU author(s): Dr Kenneth Wright

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Abstract

This paper shows that a matrix related to the n-point collocation solution of mth order ordinary differential equations using global polynomials has maximum norm which tends, as n → to the maximum norm of an operator related to the differential equation if the collocation points are chosen as the zeros of certain orthogonal polynomials. The results justify a simple a posteriori estimate for the error in the mth derivative of the corresponding solution.This result is a consequence of a stronger result that the norm of the difference between the matrix mentioned above and another matrix associated with the differential equation tends to zero as n →.

Publication metadata

Author(s): Wright K

Publication type: Article

Publication status: Published

Journal: IMA Journal of Numerical Analysis

Year: 1984

Volume: 4

Issue: 2

Pages: 185-202

ISSN (print): 0272-4979

ISSN (electronic): 1464-3642

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/imanum/4.2.185

DOI: 10.1093/imanum/4.2.185

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