Numerical Integration--Recent Developments, Software and Applications.

Abstract

Theoretical Aspects of One-Dimensional Quadrature.- The convergence of noninterpolatory product integration rules.- Some quadrature rules for finite trigonometric and related integrals.- Modified Clenshaw-Curtis integration and applications to numerical computation of integral transforms.- Fast generation of quadrature rules with some special properties.- Quadrature methods for the determination of zeros of transcendental functions - a review.- Computation of the index of an analytic function.- Approximate computation of strongly oscillatory integrals with compound precision.- Bounds and approximations for the zeros of classical orthogonal polynomials. Their use in generating quadrature rules..- Indefinite integration formulas based on the sinc expansion.- On positive quadrature rules.- Quadrature rules with end-point corrections - comments on a paper by Garloff, Solak and Szydelko.- Comparison of Gauss-Hermite and midpoint quadrature with application to the Voigt function.- Theoretical Aspects of Multiple Quadrature.- On sequences of imbedded integration rules.- Asymptotic expansions and their applications in numerical integration.- Construction of three-dimensional cubature formulae with points on regular and semi-regular polytopes.- Construction of sequences of embedded cubature formulae for circular symmetric planar regions.- On the construction of higher degree three dimensional embedded integration rules.- Fully symmetric integration rules for the unit four-cube.- On the construction of cubature formulae with few nodes using Groebner bases.- Quasi-random sequences for optimization and numerical integration.- Non-fortuitous, non-product, non-fully symmetric cubature structures.- Algorithms, Software and Applications.- A parallelization of adaptive integration methods.- The numerical evaluation of multiple integrals on parallel computers.- Vectorisation of one dimensional quadrature codes.- Performance of self-validating adaptive quadrature.- Using weight functions in self-validating quadrature.- On the construction of a practical Ermakov-Zolotukhin multiple integrator.- Interactive numerical quadrature.- The design of a generic quadrature library in Ada.- The integration of the multivariate normal density function for the triangular method.- Numerical integration in scalar wave scattering, with application to acoustic scattering by fish.- Software Classification and Testing.- Testing multiple integrators.- A package for testing multiple integration subroutines.- A test of some well known one dimensional general purpose automatic quadrature routines.- Development of useful quadrature software, with particular emphasis on microcomputers.- Appendix I: Final Program.- Appendix II: Discussion.- List of Participants.- List of Contributors.