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Uniform partition and the best least-squares piecewise polynomial approximation

Published online by Cambridge University Press:  17 April 2009

François Dubeau
François Dubeau
Affiliation:
Département de Mathématiques, Collège militaire royal de Saint-Jean, Saint-Jean-sur-Richelieu Québec, Canada, JOJ 1RO
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Abstract

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It is shown that the best least-squares piecewise n degree polynomial approximation of xn+1 over [a, b] is obtained for a uniform partition. Moreover the approximation is continuous for n odd and discontinuous, with equal stepsizes at the nodes, for n even.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 279 - 283
Copyright
Copyright © Australian Mathematical Society 1991

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