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Numerical Integration: Recent Developments, Software and Applications

Overview

This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks.
The papers are organized into four parts: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software; many papers are relevant...

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Paperback (Softcover reprint of the original 1st ed. 1992)
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Overview

This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks.
The papers are organized into four parts: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software; many papers are relevant to more than one category.
The workshop studied the state of the art in numerical integration (both single and multidimensional). The book contains a number of survey papers by experts on themes such as: numerical solution of integral equations, cubature formulae construction, handling singularities in finite elements, statistical applications, lattice rules, error estimates, error bounds and software.

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Editorial Reviews

Booknews
The 25 papers and long abstracts of three others survey recent progress in the theory of methods for the calculation of integrals, and how the theoretical results have been used in software development and in practical applications. They cover the broad categories of rules, error analysis, applications, and algorithms and software. Particular topics include cubature formulae construction, handling singularities in finite elements, statistical applications, lattice rules, and error bounds. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9789401051699
  • Publisher: Springer Netherlands
  • Publication date: 12/31/2013
  • Series: Nato Science Series C: (closed)
  • Edition description: Softcover reprint of the original 1st ed. 1992
  • Pages: 367
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.79 (d)

Table of Contents

Numerical Integration Rules.- A Survey of Methods for Constructing Cubature Formulae.- Linear Representations of Finite Groups and the Ideal Theoretical Construction of G-Invariant Cubature Formulas.- On the Number of Nodes of Odd Degree Cubature Formulae for Integrals with Jacobi Weights on a Simplex.- On Quadrature Formulae near Gaussian Quadrature.- Numerical Integration in High Dimensions — the Lattice Rule Approach.- Existence Theorems for Efficient Lattice Rules.- SINC Quadratures for Cauchy Principal Value Integrals.- Interpolatory Product Integration in the Presence of Singularities: Lp Theory.- The Numerical Evaluation of Definite Integrals Affected by Singularities Near the Interval of Integration.- Application of Computer Algebra Software to the Derivation of Numerical Integration Rules for Singular and Hypersingular Integrals.- Numerical Integration Error Analysis.- Remainder Estimates for Analytic Functions.- Error Bounds Based on Approximation Theory.- One Sided L1-Approximation and Bounds for Peano Kernels.- An Algebraic Study of the Levin Transformation in Numerical Integration.- Numerical Integration Applications.- Developments in Solving Integral Equations Numerically.- Numerical Integration of Singular and Hypersingular Integrals in Boundary Element Methods.- On Handling Singularities in Finite Elements.- A Robust Numerical Integration Method for 3-D Boundary Element Analysis and its Error Analysis using Complex Function Theory.- On the Numerical Calculation of Multidimensional Integrals Appearing in the Theory of Underwater Acoustics.- Statistics Applications of Subregion Adaptive Multiple Numerical Integration.- The Sinc Indefinite Integration and Initial Value Problems.- Numerical Integration Algorithms and Software.- Software for Integration over Triangles and General Simplices.- An Algorithm for Automatic Integration of Certain Singular Functions over a Triangle.- CUBPACK: Progress Report.- Parallel Cubature on Loosely Coupled Systems.- Transformation of Integrands for Lattice Rules.- DQAINT: An Algorithm for Adaptive Quadrature over a Collection of Finite Intervals.- A Note on Variable Knot, Variable Order Composite Quadrature for Integrands with Power Singularities.- Computation of Oscillatory Infinite Integrals by Extrapolation Methods.- Appendix: Final Program.- List of Participants.- List of Contributors.

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