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Titlebook: Dimensionality Reducing Expansion of Multivariate Integration; Tian-Xiao He Book 2001 Birkh?user Boston 2001 Excel.approximation theory.ha

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書目名稱Dimensionality Reducing Expansion of Multivariate Integration
編輯Tian-Xiao He
視頻videohttp://file.papertrans.cn/281/280474/280474.mp4
圖書封面Titlebook: Dimensionality Reducing Expansion of Multivariate Integration;  Tian-Xiao He Book 2001 Birkh?user Boston 2001 Excel.approximation theory.ha
描述.Multivariate integration has been a fundamental subject in mathematics, with broad connections to a number of areas: numerical analysis, approximation theory, partial differential equations, integral equations, harmonic analysis, etc. In this work the exposition focuses primarily on a powerful tool that has become especially important in our computerized age, namely, dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. To date, there is no comprehensive treatment of this subject in monograph or textbook form. ..Key features of this self-contained monograph include: ..* fine exposition covering the history of the subject ..* up-to-date new results, related to many fields of current research such as boundary element methods for solving PDEs and wavelet analysis ..* presentation of DRE techniques using a broad array of examples ..* good balance between theory and application ..* coverage of such related topics as boundary type quadratures and asymptotic expansions of oscillatory integrals ..* excellent and comprehensive bibliography and index ..This work will appea
出版日期Book 2001
關鍵詞Excel; approximation theory; harmonic analysis; numerical analysis; numerical integration; numerical quad
版次1
doihttps://doi.org/10.1007/978-1-4612-2100-5
isbn_softcover978-1-4612-7414-8
isbn_ebook978-1-4612-2100-5
copyrightBirkh?user Boston 2001
The information of publication is updating

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Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions,ree of precision of the approximate computation of oscillatory integrals will be looked at in Section 3. Section 4 will give a fast numerical computation technique shown in Bradie, Coifman, and Grossmann [2] for treating model oscillatory boundary integral operators with or without singularities in
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DREs Over Complex Domains,nctions, a double integral of an . over a complex domain can be reduced to a .. A subsequent application of the . to the contour integral yields a DRE for the double integral. Since for any given . there always exists an analytic function the real part of which is the given harmonic function, a DRE
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Balanced Arrangement of Groups of 3D Objectspositive integers. Here, function . in the integral is called a .. In this chapter, we will show that an integral of a continuous function . (.,., .; .,…, .) over a 2.-dimensional sphere or cube can be approximated by a sequence of oscillatory integrals. In particular, if the continuous function . i
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https://doi.org/10.1007/978-3-319-15245-5In this chapter, we will discuss DRE construction using the generalized integration by parts rule, DREs with algebraic precision, and the minimum estimation of the remainders in DREs with algebraic precision. Some optimal DREs will also be given. As the starting point, we will look at ., which can be considered as one-dimensional DREs.
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