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The Computer Journal 1975 18(1):77-80; doi:10.1093/comjnl/18.1.77
© 1975 by British Computer Society
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The use of derivatives in the optimisation of the truncation error of polynomial approximations

F. Oliveira-Pinto *

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

The truncation error of polynomial interpolations can be written as a form expressible as the product of two functions so that one factor depends only on the points we use for the interpolations, while the other depends essentially on the function we aim to approximate. To optimise this error term in a min-max sense, we concentrate on the first part and introduce extra degrees of freedom by use of extra information in the form of values of derivatives at some of the interpolation points. This paper gives a discussion of the ‘best’ choice of the extra information and the implications of such ‘extended’ approximations.

Received April 1973.

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


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