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Some contributions to the theory and application of polynomial approximation

The fundamental theorem, as far as this work is concerned, is Weierstrass' theorem (1885) on the approximability of continuous functions by polynomials. Since the time of Weierstrass (1815-97) and his equally important contemporary Chebyshev (1821-94), the topic of approximation has grown enormously into a subject of considerable interest to both pure and applied mathematicians. The subject matter of this thesis, being exclusively concerned with polynomial approximations to a single-valued, function of one real variable, is on the side of 'applied' side of approximation theory. The first chapter lists the definitions and theorems required subsequently. Chapter is devoted to estimates for the maximum error in minimax polynomial approximations. Extensions of this are used to obtain crude error estimates for cubic spline approximations. The following chapter extends the minimax results to deal also with best L[sub]p polynomial approximations, which include beat least squares (L2) and best modulus of integral (L1) approximations as special cases. Chapter 4 is different in character. It is on the practical problem of approximating to convex or nearly convex data.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:750070
Date January 1969
CreatorsPhillips, George McArtney
ContributorsCurle, S. N.
PublisherUniversity of St Andrews
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttp://hdl.handle.net/10023/13883

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