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

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The Integration and DREs of Rapidly Oscillating Functions,l can be reduced to a one-dimensional oscillatory integral with, of course, a remainder. Hence, we need to give approximation expansions of one-dimensional oscillatory integrals. A basic expansion formula is shown as follows (see Section 4).

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Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions,ebesgue integrals to one-dimensional integrals of measure functions. This technique is particularly useful for integrands that are highly oscillatory in character or are singular. The corresponding error analysis for finding measure functions will be given in Section 6.

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Fast Heuristic for Particle Packing Problemr which some given DREs and/or quadrature formulas of double integrals hold. Section 4 will discuss some additional topics on DREs over complex domains such as the construction of a Schwarz function regular in a slit region and applications of DREs in Fourier expansion.

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DREs Over Complex Domains,r which some given DREs and/or quadrature formulas of double integrals hold. Section 4 will discuss some additional topics on DREs over complex domains such as the construction of a Schwarz function regular in a slit region and applications of DREs in Fourier expansion.

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proximation 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 techn

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https://doi.org/10.1007/978-3-319-15245-5l also be given. In Section 3, we will show a general process to construct quadratures for boundary integrals by using periodic wavelets and the sampling theorem. Finally, several applications of DREs and BTQFs will be given in Section 5.

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