ACM Home Page
Please provide us with feedback. Feedback
An Algorithm for Automatic Integration Over a Triangle Using Nonlinear Extrapolation
Full text PdfPdf (850 KB)
Source ACM Transactions on Mathematical Software (TOMS) archive
Volume 10 ,  Issue 1  (March 1984) table of contents
Pages: 1 - 16  
Year of Publication: 1984
ISSN:0098-3500
Author
Ian Robinson  Computer Science Department, La Trobe University, Bundoora, Victoria, 3083, Australia
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 12,   Downloads (12 Months): 97,   Citation Count: 2
Additional Information:

references   cited by   collaborative colleagues  

Tools and Actions: Request Permissions Request Permissions    Review this Article  
DOI Bookmark: Use this link to bookmark this Article: http://doi.acm.org/10.1145/356068.356069
What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
CRANLEY, R AND PATTERSON, T.N.L. On the automatm numerical evaluation of definite integrals. Comput J 14, 2 (1971), 189-198.
2
 
3
DE DONCKER, E. New Euler-Maclaurin expansions and their application to quadrature over the s-dimensional simplex. Math. Comput 33, 147 (1979), 1003-1018.
 
4
DE DONCKER, E. Numerical integration and asymptotic expansmns. Ph.D. thesis, Katholieke Universiteit Leuven, Belgium (1980).
5
 
6
GENZ, A.C. An adaptive multidimensional integration algorithm with extrapolation. Math. Institute Univ. of Kent at Canterbury (1973).
 
7
GENZ, A.C. The approximate calculation of multidimensional integrals using extrapolation methods. Ph.D. thesis, Univ. of Kent at Canterbury (1975).
 
8
HAEGEMANS, A. Algorithm 34. An algorithm for automatic integration over a triangle. Computing 19 (1977), 179-187.
 
9
KAHANER, D.K. Numerical quadrature by the -algorithm. Math. Comput. 26, 119 (1972), 689- 693.
 
10
KAHANER, D.K. AND WELLS, M.B. An algorithm for N-dimensional adaptive quadrature using advanced programming techniques. Tech Memo. LA-UR 76-2310, Los Alamos Scientific Laboratories, Los Alamos, New Mexico (1977).
11
 
12
LYNESS, J.N. An error functional expansion for N-dimensional quadrature with an integrand function singular at a point. Math. Comput 30, 133 (1976), 1-23.
 
13
LYNESS, J.N, Quadrature over a simplex: Part I. A representation for the integrand function. SIAM. J Numer Anal. 15, I (1978), 122-133.
 
14
LYNESS, J.N. Quadrature over a simplex: Part If. A representation for the error functional. SIAM J Numer Anal 15, 5 (1978), 870-887.
 
15
LYNESS, J.N. AND GENZ, A.C. On simplex trapezoidal rule families. SIAM J. Numer. Anal. 17, 1 (1980), 126-147.
 
16
LYNESS, J.N. AND JESPERSEN, D. Moderate degree symmetric quadrature rules for the triangle J Inst Maths. Apphes 15 (1975), 19-32.
 
17
LYNESS, J.N. AND MONEGATO, G. Quadrature error functional expansions for the simplex when the integrand function has singularities at vertices. Math. Comp 34, 149 (1980), 213-225
 
18
LYNESS, J.N. AND PURl, K.K. The Euler-Maclaurin expansion for the simplex. Math. Comp. 27, 122 (1973), 273-293.
19
 
20
PIESSENS, R. A quadrature routine with roundoff error guard. Report TWl7, Appl. Math. and Progr., Katholieke Umversteit Leuven, Belgmm (1974).
 
21
PIESSENS, R., DE DONCKER, E., UBERHUBER, C. AND KAHANER, D.K. QUADPACK--A Subroutine Package for Automatic Integratwn. Springer Series in Computatmnal Mathematics 1 (1983), Springer-Verlag, N.Y.
 
22
STROUD, A.H. Approximate Caleulatmn of Multiple Integrals, Prentice-Hall, Englewood Cliffs, N.J. (1971), 118-119.
 
23
VAN DOOREN, P. AND DE RIDDER, L. An adaptive algorithm for numerical integration over an N-dimensional cube. J Comput. Appl. Math. 2 (1976), 207-217.
 
24
WYNN, P. On a device for computing the em(Sn) transformation. Mathematical Tables and Aids to Computing 10 (1956), 91-96.