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Approximation theory
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Details
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby. Note that what is meant by best and simpler will depend on the application. A closely related topic is the approximation of functions by generalized Fourier series, that is, approximations based upon summation of a series of terms based upon orthogonal polynomials. One problem of particular interest is that of approximating a function in a computer mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with polynomial or rational (ratio of polynomials) approximations. The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130294090
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T8mm
- Jahr 2010
- EAN 9786130294090
- Format Fachbuch
- ISBN 978-613-0-29409-0
- Titel Approximation theory
- Untertitel Function (mathematics), Approximation, Quantitative property, Approximation error, Generalized Fourier series, Orthogonal polynomials, Computer, Polynomial, Rational function, Floating point
- Gewicht 219g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 136
- Genre Mathematik
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