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The Tchebysheffian approximation of one rational function by another

Published online by Cambridge University Press:  24 October 2008

A. Talbot
A. Talbot
Affiliation:
Imperial College, London
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Extract

In a previous paper we discussed a uniform algebraic method of solution of problems in which a prescribed real rational function (or polynomial) g(x) was to be approximated in a given finite interval by a real rational function (or polynomial)f(x) with prescribed numerator and denominator degrees, the approximation being Tchebysheffian, i.e. such as to make the ‘deviation’ of f, max |f − g| in the interval, as small as possible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 877 - 890
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1)Talbot, A.On a class of Tchebysheffian approximation problems solvable algebraically. Proc. Cambridge Philos. Soc. 58 (1962), 244–267.CrossRefGoogle Scholar
(2)Tchebysheff, P. L.Sur les questions de minima qui se rattachent à la représentation approchée des functions. Mem. Acad. Imp. Sci. St Pétersburg, IX (1859), 201–291; Oeuvres, I, 273–378.Google Scholar