Quadpack A Subroutine Package for Automatic Integration
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.
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FUNCTION SUBPROGRAM DEFINING THE INTEGRAND FUNCTION OR A FACTOR OF THE INTEGRAND FUNCTION
A,B
LIMITS OF THE INTEGRATION INTERVAL
EPSABS
ABSOLUTE ACCURACY REQUESTED
EPSREL
RELATIVE ACCURACY REQUESTED
KEY
KEY FOR CHOICE OF LOCAL INTEGRATION RULE IN QAG (SEE P. 137)
NPTS2 POINTS
DETERMINE THE USER PROVIDED BREAK POINTS IN QAGP (SEE P. 156)
BOUND INF
DETERMINE THE INTEGRATION INTERVAL IN QAGI (SEE P. 167)
OMEGA INTEGR
PARAMETERS OF THE WEIGHT FUNCTION IN QAWO AND QAWF (SEE P. 176 AND P. 180)
ALFA BETA INTEGR
PARAMETERS OF THE WEIGHT FUNCTION IN QAWS (SEE P. 192)
C
PARAMETER IN THE WEIGHT FUNCTION IN QAWC (SEE P. 203)
ON RETURN RESULT
APPROXIMATION TO THE INTEGRAL
ABSERR
ESTIMATE OF THE ABSOLUTE ERROR
NEVAL
NUMBER OF INTEGRAND EVALUATIONS
IER
PARAMETER PROVIDING INFORMATION ON THE TERMINATION OF THE ROUTINE
Springer Series in Computational Mathematics
1
Editorial Board R. Graham, Murray Hill J. Stoer, WOrzburg R. Varga, Cleveland
R. Piessens E. de Doncker-Kapenga
C. w. Oberhuber D. K Kahaner
QUADPACK A Subroutine Package for Automatic Integration
With 26 Figures
Springer-Verlag Berlin Heidelberg New York Tokyo 1983
Robert Piessens Computer Science Department, University of Leuven, Celestijnenlaan 200 A, 3030 Heverlee, Belgium Elise de Doncker-Kapenga Computer Science Department, Western Michigan University, Kalamazoo, Mi 49008, USA Christoph W. Oberhuber Department of Applied and Numerical Mathematics, Technical University Vienna, Gusshausstr. 27-29, 1040 Wien, Austria David K. Kahaner National Bureau of Standards, Washington, DC 20234, USA
AMS Subject Classifications (1980): 65 D 30
ISBN-13:978-3-540-12553-2
e-ISBN-13:978-3-642-61786-7
DOl: 10.1007/978-3-642-61786-7 Library of Congress Cataloging in Publication Data. Main entry under title: QUAD PACK : a subroutine package for automatic integration. (Springer series in computational mathematics; 1) Includes bibliographical references. 1. QUADPACK (Computer programs) 2. Numerical integration-Computer programs. I. Piessens, R. II. Series. QA299.3.Q36. 1983. 515.4'028'5425. 83-10359 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1983
Reprint of the original edition 1983 214113140-543210
Acknowledgement
We owe the financial support to the "Nationaal Fonds pelijk
voor
Wetenschap-
Onderzoek" and the "Onderzoeksfonds van de Katholieke Universi-
teit van Leuven". We thank Branders
Philip
Rabinowitz,
James
Lyness,
Ann
for their comments and suggestions manuscript or the routines and their results.
Haegemans regarding
and
May
either the
We thank Brian Ford and the NAG staff, and Bob Huddleston, for th
