論文

査読有り
2005年4月

Gaussian quadrature rule for arbitrary weight function and interval

COMPUTER PHYSICS COMMUNICATIONS
  • H Fukuda
  • ,
  • M Katuya
  • ,
  • EO Alt
  • ,
  • AV Matveenko

167
2
開始ページ
143
終了ページ
150
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1016/j.cpc.2004.12.010
出版者・発行元
ELSEVIER SCIENCE BV

A program for calculating abscissas and weights of Gaussian quadrature rules for arbitrary weight functions and intervals is reported. The program is written in Mathematica. The only requirement is that the moments of the weight function can be evaluated analytically in Mathematica. The result is a FORTRAN subroutine ready to be utilized for quadrature.
Program summary
Title of program: AWGQ
Catalogue identifier: ADVB
Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVB
Program obtained from: CPC Program Library, Queens University, Belfast, N. Ireland
Computer for which the program is designed and others on which it has been tested:
Computers: Pentium IV 1.7 GHz processor
Installations: 512 MB RAM
Operating systems or monitors under which the program has been tested: Windows XP
Programming language used: Mathematica 4.0
No. of processors used: 1
Has the code been vectorized or parallelized?: No
No. of lines in distributed program, including test data, etc.: 1076
No. of bytes in distributed program, including test data, etc.: 32 681
Operating systems under which program has been tested: FORTRAN
Distribution format: tar.gz
Nature of physical problem: Integration of functions.
Method of solution: The recurrence relations defining the orthogonal polynomials for arbitrary weight function and integration interval are written in matrix form. The abscissas and weights for the corresponding Gaussian quadrature are found from the solution of the eigenvalue equation for the tridiagonal symmetric Jacobi matrix.
Restrictions on the complexity of the problem: The program is applicable if the moments of the weight function can be evaluated analytically in Mathematica. For our test example the degee of the Gaussian quadrature cannot not he larger than 96,
Typical running time: The running time of the test run is about 1 [s] with a Pentium IV 1.7 GHz processor, (c) 2005 Elsevier B.V. All rights reserved.

Web of Science ® 被引用回数 : 4

リンク情報
DOI
https://doi.org/10.1016/j.cpc.2004.12.010
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000228421500007&DestApp=WOS_CPL