Titlebook: Numerical Integration; Recent Developments, Terje O. Espelid,Alan Genz Book 1992 Springer Science+Business Media Dordrecht 1992 Numerical i

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On the Number of Nodes of Odd Degree Cubature Formulae for Integrals with Jacobi Weights on a Simpledepending on the moments of the integral considered. For the integrals in question the determination of this matrix and the computation of its rank is hard. However for constant weight function G.G. Rasputin succeeded in determining the rank. The approach presented here is based on the recursion for

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Existence Theorems for Efficient Lattice Rules these methods depends on the proper choice of an integration lattice. In this paper we present results that guarantee the existence of integration lattices for which the corresponding lattice rules yield small error bounds. These results improve or generalize earlier existence theorems in this area

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Sinc Quadratures for Cauchy Principal Value Integralsomplex plane. Under suitable assumptions on ., the quadrature errors are of order , where . is the number of quadrature nodes and . is a positive constant independent of .. Special consideration is given to SINC quadratures for Cauchy principal value integrals over (—∞, ∞), (0, ∞), and (—1, 1).

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The Numerical Evaluation of Definite Integrals Affected by Singularities Near the Interval of Integrariable, has singularities near the real axis. The main method is concerned with the case when the singularities are poles of arbitrary order, but an extension to deal with branch singularities is briefly considered. A modification for the evaluation of Cauchy principal value integrals is also descr

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Application of Computer Algebra Software to the Derivation of Numerical Integration Rules for Singulhe corresponding hypersingular (finite-part) integrals (like M angler-type integrals). The modern and powerful computer algebra system MATHEMATICA was employed in this task. A case of the Gauss-Chebyshev quadrature rule as well as the Gauss-Legendre quadrature rule are used for the illustration of t