Numerical Integration: Recent Developments, Software and Applications - Hardcover

by Terje O. Espelid (Author), NATO Advanced Research Workshop on Numer (Author), North Atlantic Treaty Organization (Author)

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.