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Asymptotic Properties of Collocation Matrix Norms 2: Piecewise Polynomial Approximation

Lookup NU author(s): Dr Clive Gerrard, Dr Kenneth Wright

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Abstract

This paper considers a matrix related to the solution by piecewise polynomial collocation using n subintervals of an mth-order ordinary differential boundary-value problem. It is shown that if the maximum subinterval size tends to zero as Formula the matrix norm tends to the norm of an operator related to the differential equation, under the assumption that the collocation points in each subinterval are assumed to be distributed identically and their associated interpolatory quadrature weights are positive.

Publication metadata

Author(s): Gerrard C, Wright K

Publication type: Article

Publication status: Published

Journal: IMA Journal of Numerical Analysis

Year: 1984

Volume: 4

Issue: 3

Pages: 363-373

ISSN (print): 0272-4979

ISSN (electronic): 1464-3642

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1093/imanum/4.3.363

DOI: 10.1093/imanum/4.3.363

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