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Meinardus G. Approximation of functions: Theory and numerical methods

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Meinardus G. Approximation of functions: Theory and numerical methods
Springer, 1967. — 206 p.
It has only been in the past few years that those parts of approximation theory which can be applied to numerical problems have been strongly developed. The idea of obtaining a (in some sense) best approximation of a function gained considerable importance with the application of electronic computers. Some of the theoretical fundamentals necessary for practical problems can be found scattered about in a few books. However, by far the greatest portion of the theoretical and practical investigations can be studied only in the original papers. This provides the purpose of this book: to collect essential results of approximation theory which on the one hand makes possible a fast introduction to the modern development of this area, and on the other hand provides a certain completeness to the problem area of Tchebycheff approximation — not to imply by any means that a comprehensive survey of the literature is attempted. The material has been chosen from the subjective standpoint of its importance for applications. This also applies, for example, to the asymptotic investigations of § 3, since I am of the opinion that even in numerical approximation some thought should at least be given to what asymptotic precision can be expected. I have confined myself almost exclusively to the theory of uniform approximation since it has by far the greatest practical importance.
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