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 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.

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Content:
Front Matter....Pages i-xiii
The Convergence of Noninterpolatory Product Integration Rules....Pages 1-16
Some Quadrature Rules for Finite Trigonometric and Related Integrals....Pages 17-33
Modified Clenshaw-Curtis Integration and Applications to Numerical Computation of Integral Transforms....Pages 35-51
Fast Generation of Quadrature Rules with Some Special Properties....Pages 53-60
Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review....Pages 61-82
Computation of the Index of an Analytic Function....Pages 83-90
Approximate Computation of Strongly Oscillatory Integrals with Compound Precision....Pages 91-101
Bounds and Approximations for the Zeros of Classical Orthogonal Polynomials. Their use in Generating Quadrature Rules....Pages 103-104
Indefinite Integration Formulas Based on the Sinc Expansion....Pages 105-106
On Positive Quadrature Rules....Pages 107-108
Quadrature Rules with End-Point Corrections: Comments on a Paper by Garloff, Solak and Szydelko....Pages 109-109
Comparison of Gauss-Hermite and Midpoint Quadrature with Application to the Voigt Function....Pages 111-112
On Sequences of Imbedded Integration Rules....Pages 113-139
Asymptotic Expansions and Their Applications in Numerical Integration....Pages 141-151
Construction of Three-Dimensional Cubature Formulae with Points on Regular and Semi-Regular Polytopes....Pages 153-163
Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regions....Pages 165-172
On the Construction of Higher Degree Three Dimensional Embedded Integration Rules....Pages 173-174
Fully Symmetric Integration Rules for the Unit Four-Cube....Pages 175-176
On the Construction of Cubature Formulae with Few Nodes Using Groebner Bases....Pages 177-192
Quasi-Random Sequences for Optimization and Numerical Integration....Pages 193-203
Non-Fortuitous, Non-Product, Non-Fully Symmetric Cubature Structures....Pages 205-205
A Parallelization of Adaptive Integration Methods....Pages 207-218
The Numerical Evaluation of Multiple Integrals on Parallel Computers....Pages 219-229
Vectorisation of One Dimensional Quadrature Codes....Pages 231-238
Performance of Self-validating Adaptive Quadrature....Pages 239-259
Using Weight Functions in Self-Validating Quadrature....Pages 261-268
On the Construction of a Practical Ermakov-Zolotukhin Multiple Integrator....Pages 269-290
Interactive Numerical Quadrature....Pages 291-306
The Design of a Generic Quadrature Library in Ada....Pages 307-319
The Integration of the Multivariate Normal Density Function for the Triangular Method....Pages 321-328
Numerical Integration in Scalar Wave Scattering, with Application to Acoustic Scattering by Fish....Pages 329-329
Testing Multiple Integrators....Pages 331-335
A Package for Testing Multiple Integration Subroutines....Pages 337-340
A Test of Some Well Known One Dimensional General Purpose Automatic Quadrature Routines....Pages 341-342
Development of Useful Quadrature Software, with Particular Emphasis on Microcomputers....Pages 343-369
Back Matter....Pages 371-394

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Content:
Front Matter....Pages i-xiii
The Convergence of Noninterpolatory Product Integration Rules....Pages 1-16
Some Quadrature Rules for Finite Trigonometric and Related Integrals....Pages 17-33
Modified Clenshaw-Curtis Integration and Applications to Numerical Computation of Integral Transforms....Pages 35-51
Fast Generation of Quadrature Rules with Some Special Properties....Pages 53-60
Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review....Pages 61-82
Computation of the Index of an Analytic Function....Pages 83-90
Approximate Computation of Strongly Oscillatory Integrals with Compound Precision....Pages 91-101
Bounds and Approximations for the Zeros of Classical Orthogonal Polynomials. Their use in Generating Quadrature Rules....Pages 103-104
Indefinite Integration Formulas Based on the Sinc Expansion....Pages 105-106
On Positive Quadrature Rules....Pages 107-108
Quadrature Rules with End-Point Corrections: Comments on a Paper by Garloff, Solak and Szydelko....Pages 109-109
Comparison of Gauss-Hermite and Midpoint Quadrature with Application to the Voigt Function....Pages 111-112
On Sequences of Imbedded Integration Rules....Pages 113-139
Asymptotic Expansions and Their Applications in Numerical Integration....Pages 141-151
Construction of Three-Dimensional Cubature Formulae with Points on Regular and Semi-Regular Polytopes....Pages 153-163
Construction of Sequences of Embedded Cubature Formulae for Circular Symmetric Planar Regions....Pages 165-172
On the Construction of Higher Degree Three Dimensional Embedded Integration Rules....Pages 173-174
Fully Symmetric Integration Rules for the Unit Four-Cube....Pages 175-176
On the Construction of Cubature Formulae with Few Nodes Using Groebner Bases....Pages 177-192
Quasi-Random Sequences for Optimization and Numerical Integration....Pages 193-203
Non-Fortuitous, Non-Product, Non-Fully Symmetric Cubature Structures....Pages 205-205
A Parallelization of Adaptive Integration Methods....Pages 207-218
The Numerical Evaluation of Multiple Integrals on Parallel Computers....Pages 219-229
Vectorisation of One Dimensional Quadrature Codes....Pages 231-238
Performance of Self-validating Adaptive Quadrature....Pages 239-259
Using Weight Functions in Self-Validating Quadrature....Pages 261-268
On the Construction of a Practical Ermakov-Zolotukhin Multiple Integrator....Pages 269-290
Interactive Numerical Quadrature....Pages 291-306
The Design of a Generic Quadrature Library in Ada....Pages 307-319
The Integration of the Multivariate Normal Density Function for the Triangular Method....Pages 321-328
Numerical Integration in Scalar Wave Scattering, with Application to Acoustic Scattering by Fish....Pages 329-329
Testing Multiple Integrators....Pages 331-335
A Package for Testing Multiple Integration Subroutines....Pages 337-340
A Test of Some Well Known One Dimensional General Purpose Automatic Quadrature Routines....Pages 341-342
Development of Useful Quadrature Software, with Particular Emphasis on Microcomputers....Pages 343-369
Back Matter....Pages 371-394
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