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The Computer Journal 1973 16(4):375-379; doi:10.1093/comjnl/16.4.375
© 1973 by British Computer Society
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Generalised Chebyshev polynomials and their use in numerical approximation*

F. Oliveira-Pinto §

Computer Laboratory, University of Cambridge, Corn Exchange Street, Cambridge, UK

The concept of generalised Chebyshev polynomials is introduced in connection with the interpolation by a linear form

[equation: see PDF]

of a real function Z(x), defined over an arbitrary prescribed set of discrete points. In this form both ak -> 0, 1,..., q and ‘basic’ functions {varphi}k(x), k -> 0,1, ..., q are defined to minimise in the Chebyshev sense a known part of the corresponding truncation error {epsilon}q(x). It is shown that these generalised polynomials become, for the case of equidistant sampling points, the classical Cosine Trigonometric polynomials.

The advantages in the use of these generalised Chebyshev polynomials versus the traditional Chebyshev ones are emphasised in two numerical examples.

Received August 1972.

* This research was possible due to the annual grant No. 663 of the Science Department of the Gulbenkian Foundation.

§ Computer Laboratory, University of Cambridge, Corn Exchange Street, Cambridge CB2 3QG


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