Quadpack

A Subroutine Package for Automatic Integration

  • Robert Piessens
  • Elise de Doncker-Kapenga
  • Christoph W. Überhuber
  • David K. Kahaner

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 1)

Table of contents

  1. Front Matter
    Pages N1-VIII
  2. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 1-8
  3. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 9-55
  4. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 56-74
  5. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 75-111
  6. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 112-127
  7. Robert Piessens, Elise de Doncker-Kapenga, Christoph W. Überhuber, David K. Kahaner
    Pages 128-294
  8. Back Matter
    Pages 295-304

About this book

Introduction

1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi­ cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo­ nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua­ tion of integrals. However, most routine integrals in practical scien­ tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.

Keywords

Numerical integration Numerische Integration QUADPACK algorithms numerical quadrature

Authors and affiliations

  • Robert Piessens
    • 1
  • Elise de Doncker-Kapenga
    • 2
  • Christoph W. Überhuber
    • 3
  • David K. Kahaner
    • 4
  1. 1.Computer Science DepartmentUniversity of LeuvenHeverleeBelgium
  2. 2.Computer Science DepartmentWestern Michigan UniversityKalamazooUSA
  3. 3.Department of Applied and Numerical MathematicsTechnical University ViennaWienAustria
  4. 4.National Bureau of StandardsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61786-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 1983
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-12553-2
  • Online ISBN 978-3-642-61786-7
  • Series Print ISSN 0179-3632
  • About this book