Ebook: Numerical Integration: Recent Developments, Software and Applications

This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop­ ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.

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Content:
Front Matter....Pages i-xii
A Survey of Methods for Constructing Cubature Formulae....Pages 1-24
Linear Representations of Finite Groups and The Ideal Theoretical Construction of G-Invariant Cubature Formulas....Pages 25-35
On the Number of Nodes of Odd Degree Cubature Formulae for Integrals with Jacobi Weights on a Simplex....Pages 37-44
On Quadrature Formulae Near Gaussian Quadrature....Pages 45-54
Numerical Integration in High Dimensions — the Lattice Rule Approach....Pages 55-69
Existence Theorems for Efficient Lattice Rules....Pages 71-80
Sinc Quadratures for Cauchy Principal Value Integrals....Pages 81-92
The Numerical Evaluation of Definite Integrals Affected by Singularities Near the Interval of Integration....Pages 93-109
Application of Computer Algebra Software to the Derivation of Numerical Integration Rules for Singular and Hypersingular Integrals....Pages 111-120
Remainder Estimates for Analytic Functions....Pages 121-131
Error Bounds Based on Approximation Theory....Pages 133-145
One Sided L1-Approximation and Bounds for Peano Kernels....Pages 147-163
An Algebraic Study of the Levin Transformation in Numerical Integration....Pages 165-174
Developments in Solving Integral Equations Numerically....Pages 175-186
Numerical Integration of Singular and Hypersingular Integrals in Boundary Element Methods....Pages 187-201
On Handling Singularities in Finite Elements....Pages 203-218
A Robust Numerical Integration Method for 3-D Boundary Element Analysis and Its Error Analysis using Complex Function Theory....Pages 219-233
On the Numerical Calculation of Multidimensional Integrals Appearing in the Theory of Underwater Acoustics....Pages 235-248
Statistics Applications of Subregion Adaptive Multiple Numerical Integration....Pages 249-265
Sinc Indefinite Integration and Initial Value Problems....Pages 267-280
Software for Integration Over Triangles and General Simplices....Pages 281-282
An Algorithm for Automatic Integration of Certain Singular Functions Over a Triangle....Pages 283-294
Cubpack: Progress Report....Pages 295-304
Parallel Cubature on Loosely Coupled Systems....Pages 305-315
Transformation of Integrands for Lattice Rules....Pages 317-327
DQAINT: An Algorithm for Adaptive Quadrature Over a Collection of Finite Intervals....Pages 329-340
A Note On Variable Knot, Variable Order Composite Quadrature For Integrands With Power Singularities....Pages 341-342
Computation of Oscillatory Infinite Integrals by Extrapolation Methods....Pages 343-347
Back Matter....Pages 349-351
....Pages 353-367