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- Approximation_theory abstract "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.Narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.".
- Approximation_theory thumbnail Logerror.png?width=300.
- Approximation_theory wikiPageExternalLink index.html?pg=233.
- Approximation_theory wikiPageExternalLink SAT.
- Approximation_theory wikiPageExternalLink hat.
- Approximation_theory wikiPageExternalLink ATAP.
- Approximation_theory wikiPageID "1092713".
- Approximation_theory wikiPageRevisionID "583643324".
- Approximation_theory hasPhotoCollection Approximation_theory.
- Approximation_theory subject Category:Approximation_theory.
- Approximation_theory subject Category:Numerical_analysis.
- Approximation_theory comment "In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.".
- Approximation_theory label "Approximation theory".
- Approximation_theory label "Teoria dell'approssimazione".
- Approximation_theory label "Teoría de la aproximación".
- Approximation_theory label "Théorie de l'approximation".
- Approximation_theory label "Теория приближений".
- Approximation_theory label "逼近理论".
- Approximation_theory sameAs Teoría_de_la_aproximación.
- Approximation_theory sameAs Théorie_de_l'approximation.
- Approximation_theory sameAs Teoria_dell'approssimazione.
- Approximation_theory sameAs m.045bns.
- Approximation_theory sameAs Q774123.
- Approximation_theory sameAs Q774123.
- Approximation_theory wasDerivedFrom Approximation_theory?oldid=583643324.
- Approximation_theory depiction Logerror.png.
- Approximation_theory isPrimaryTopicOf Approximation_theory.