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Boundary Type Quadrature Formulas with Algebraic Precision

In: Dimensionality Reducing Expansion of Multivariate Integration

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  • Tian-Xiao He

    (Illinois Wesleyan University, Department of Mathematics & Computer Sience)

Abstract

First, in Section 1, we will show that a DRE can be made an effective tool for constructing BTQFs with preassigned algebraic precision. Section 2 will discuss the construction of BTQFs with homogeneous precision. General Hermite formulas and a class of BTQFs that has the highest possible degrees of algebraic precision will 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.

Suggested Citation

  • Tian-Xiao He, 2001. "Boundary Type Quadrature Formulas with Algebraic Precision," Springer Books, in: Dimensionality Reducing Expansion of Multivariate Integration, chapter 0, pages 25-78, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2100-5_2
    DOI: 10.1007/978-1-4612-2100-5_2
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