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1964•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

The Tchebysheffian approximation of one rational function by another

A. Talbot

Open publisher page 5 citations

Abstract

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.

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What this paper is about

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.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

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.

Key concepts: Rational function, Interval (graph theory), Mathematics, Polynomial and rational function modeling, Polynomial, Function (biology), Algebraic function, Algebraic number

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