Numerical Integration

1. Front Matter

   Pages i-xiii

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2. Theoretical Aspects of One-Dimensional Quadrature

   1. The Convergence of Noninterpolatory Product Integration Rules

      • Philip Rabinowitz

      Pages 1-16

   2. Some Quadrature Rules for Finite Trigonometric and Related Integrals

      • J. N. Lyness

      Pages 17-33

   3. Modified Clenshaw-Curtis Integration and Applications to Numerical Computation of Integral Transforms

      • R. Piessens

      Pages 35-51

   4. Fast Generation of Quadrature Rules with Some Special Properties

      • T. H. Baker, M. S. Derakhshan

      Pages 53-60

   5. Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review

      • Nikolaos I. Ioakimidis

      Pages 61-82

   6. Computation of the Index of an Analytic Function

      • M. P. Carpentier

      Pages 83-90

   7. Approximate Computation of Strongly Oscillatory Integrals with Compound Precision

      • L. C. Hsu, Y. S. Zhou

      Pages 91-101

   8. Bounds and Approximations for the Zeros of Classical Orthogonal Polynomials. Their use in Generating Quadrature Rules

      • Luigi Gatteschi

      Pages 103-104

   9. Indefinite Integration Formulas Based on the Sinc Expansion

      • S. Haber

      Pages 105-106

   10. On Positive Quadrature Rules

       • Hans Joachim Schmid

       Pages 107-108

   11. Quadrature Rules with End-Point Corrections: Comments on a Paper by Garloff, Solak and Szydelko

       • William Squire

       Pages 109-109

   12. Comparison of Gauss-Hermite and Midpoint Quadrature with Application to the Voigt Function

       • William Squire

       Pages 111-112

3. Theoretical Aspects of Multiple Quadrature

   1. On Sequences of Imbedded Integration Rules

      • Philip Rabinowitz, Jaroslav Kautsky, Sylvan Elhay, John C. Butcher

      Pages 113-139

   2. Asymptotic Expansions and Their Applications in Numerical Integration

      • Elise de Doncker-Kapenga

      Pages 141-151

   3. Construction of Three-Dimensional Cubature Formulae with Points on Regular and Semi-Regular Polytopes

      • Ann Haegemans, Ronald Cools

      Pages 153-163

   4. Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regions

      • Ronald Cools, Ann Haegemans

      Pages 165-172

   5. On the Construction of Higher Degree Three Dimensional Embedded Integration Rules

      • Jarle Berntsen, Terje O. Espelid

      Pages 173-174

   6. Fully Symmetric Integration Rules for the Unit Four-Cube

      • T. Sorevik, T. O. Espelid

      Pages 175-176

   7. On the Construction of Cubature Formulae with Few Nodes Using Groebner Bases

      • H. Michael Möller

      Pages 177-192

This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Developments, Software and Applications', held at Dalhousie University, Halifax, Canada, August 11-15, 1986. The Workshop was attended by thirty-six scientists from eleven NATO countries. Thirteen invited lectures and twenty-two contributed lectures were presented, of which twenty-five appear in full in this volume, together with extended abstracts of the remaining ten. It is more than ten years since the last workshop of this nature was held, in Los Alamos in 1975. Many developments have occurred in quadrature in the intervening years, and it seemed an opportune time to bring together again researchers in this area. The development of QUADPACK by Piessens, de Doncker, Uberhuber and Kahaner has changed the focus of research in the area of one dimensional quadrature from the construction of new rules to an emphasis on reliable robust software. There has been a dramatic growth in interest in the testing and evaluation of software, stimulated by the work of Lyness and Kaganove, Einarsson, and Piessens. The earlier research of Patterson into Kronrod extensions of Gauss rules, followed by the work of Monegato, and Piessens and Branders, has greatly increased interest in Gauss-based formulas for one-dimensional integration.

• Approximation
• algorithms
• classification
• computer
• optimization

• Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Canada

  Patrick Keast

• Departments of Mathematics and Engineering Mechanics, University of Kentucky, Lexington, USA

  Graeme Fairweather

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