-
- 1
-
J. Berntsen, T.O. Espelid, and A. Genz.
An adaptive algorithm for the approximate calculation of
multiple integrals.
ACM Trans. Math. Softw., 17(4). pp. 437-451, 1991.
- 2
-
J. Berntsen and T.O. Espelid.
Error estimation in automatic quadrature routines.
ACM Trans. Math. Softw., 17(2), pp. 233-252, 1991.
- 3
-
J. Berntsen and T.O. Espelid.
Algorithm 706: DCUTRI: An algorithm for adaptive cubature
over a collection of triangles.
ACM Trans. Math. Softw., 19, pp. 329-342, 1993.
- 4
-
J. Berntsen, R. Cools and T.O. Espelid.
Algorithm 720: An algorithm for adaptive
cubature over a collection of 3-dimensional simplices.
ACM Trans. Math. Softw., 19, pp. 320-332, 1993.
- 5
-
A.G. Buckley.
Conversion to Fortran 90: a case study.
ACM Trans. Math. Softw., 20(3), pp. 308-353, 1994.
- 6
-
R. Cools and A. Haegemans.
CUBPACK: Progress report.
in Numerical Integration,
T.O. Espelid and A. Genz (Eds.), Kluwer Academic Publishers,
pp. 305-315, 1992.
- 7
-
R. Cools and B. Maerten.
A hybrid subdivision strategy for adaptive integration routines.
J. of Universal Computer Science 4, 5,
pp. 485-499.
1998.
- 8
-
R. Cools and P. Rabinowitz.
Monomial cubature rules since Stroud: a compilation.
J. Comput. Appl. Math. 48, pp. 309-326, 1993.
- 9
-
R. Cools.
Monomial cubature rules since ``Stroud'': a compilation - part 2
J. Comput. Appl. Math. 112, pp. 21-27, 1999.
- 10
-
R. Cools and A. Haegemans.
CUBPACK: a package for automatic cubature; framework description.
In preparation.
- 11
-
P.J. Davis and P. Rabinowitz.
Methods of Numerical Integration,
Academic Press, New York, 1984.
- 12
-
E. de Doncker and I. Robinson.
An algorithm for automatic integration over a triangle using
nonlinear extrapolation.
ACM Trans. Math. Soft., 10, pp. 1-16, 1984.
- 13
-
H. Engels.
Numerical Quadrature and Cubature,
Academic Press, New York, 1980.
- 14
-
T.O. Espelid and A. Genz.
On the Subdivision Strategy for Adaptive Cubature Algorithms for
Triangular Regions.
University of Bergen Department of Informatics Technical
Report No. 74, 1992.
- 15
-
K.-T. Fang and Y. Wang, Y.
Number Theoretic Methods in Statistics,
Chapman and Hall, London, 1994.
- 16
-
A. Genz.
A package for testing multiple integration subroutines,
in Numerical Integration,
P. Keast and G. Fairweather (Eds.), D. Riedel, pp. 337-340, 1987.
- 17
-
A. Genz.
An adaptive numerical integration algorithm for simplices.
in Computing in the 90s, Proceedings of the First
Great Lakes Computer Science Conference,
N. A. Sherwani, E. de Doncker and J. A. Kapenga (Eds.),
Lecture Notes in Computer Science Volume 507,
Springer-Verlag, New York, pp. 279-292, 1991.
- 18
-
A.C. Genz and A.A. Malik.
An adaptive algorithm for numerical integration
over an n-dimensional rectangular region.
J. Comp. Appl. Math., 6, pp. 295-302, 1980.
- 19
-
A. Grundmann and H.M. Möller.
Invariant integration formulas for the
n-simplex by combinatorial methods.
SIAM J. Numer. Anal. 15, pp. 282-290, 1978.
- 20
-
A. Haegemans.
An algorithm for automatic integration over a triangle.
Computing, 19, pp. 179-187, 1977.
- 21
-
D.K. Kahaner and O.W. Rechard.
TWODQD: An adaptive routine for two-dimensional integration.
J. Comp. Appl. Math. 17, pp. 215-234, 1987.
- 22
-
D.K. Kahaner and M.B. Wells.
An experimental algorithm for N-dimensional adaptive quadrature.
ACM Trans. Math. Soft.. 5, pp. 86-96, 1979.
- 23
-
P. Keast.
Cubature formulas for the sphere and simplex.
J. Inst. Maths. Applics. 23, pp. 251-264, 1979.
- 24
-
D.P. Laurie.
Algorithm 584: CUBTRI: Automatic cubature over a triangle.
ACM TOMS 8, pp. 210-218, 1982.
- 25
-
J.N. Lyness and R. Cools
A survey of numerical cubature over triangles.
Proceedings of Symposia in Applied Mathematics 48,
pp. 127-150, 1994.
- 26
-
J.N. Lyness and A. Genz.
On simplex trapezoidal rule families.
SIAM J. Numer. Anal., 17(1), pp. 126-147, 1980.
- 27
-
I.P. Mysovskikh
On a cubature formula for the simplex (Russian),
Vopros. Vycisl. i Prikl. Mat., Tashkent 51, pp. 74-90, 1978.
- 28
-
D01PAF: An automatic integration subroutine for integration over an N-simplex,
Numerical Algorithms Group Limited,
Wilkinson House, Jordan Hill Road, Oxford, United Kingdom OX2 8DR.
- 29
-
P. Silvester.
Symmetric quadrature formulas for simplices,
Math. Comp., 24, pp. 95-100, 1970.
- 30
-
A.H. Stroud.
Approximate Calculation of Multiple Integrals,
Prentice-Hall, Englewood Cliffs, New Jersey, 1971.
- 31
-
A.H. Stroud.
A Fifth Degree Integration Formula for the n-Simplex,
SIAM J Numer. Anal. 6, pp. 90-98, 1969.
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