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Some best-approximation theorems in tensor-product spaces

Published online by Cambridge University Press:  24 October 2008

W. A. Light  and
E. W. Cheney
W. A. Light
Affiliation:
University of Lancaster and University of Texas at Austin
E. W. Cheney
Affiliation:
University of Lancaster and University of Texas at Austin
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Extract

We begin by describing a concrete example from the class of problems to be considered. A continuous bivariate function f defined on the square |t| ≤ 1, |s| ≤ 1 is to be approximated by a tensor-product form involving univariate functions. For example, the approximation may be prescribed to have the form

in which the Ti are the Tchebycheff polynomials, and the coefficient functions xi(t) and yi(s) are to be chosen to achieve a good or best approximation. Will a best approximation exist? If so, how can it be obtained?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 3 , May 1981 , pp. 385 - 390
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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