论文信息 - An Experimental Algorithm for N-Dimensional Adaptive Quadrature

An Experimental Algorithm for N-Dimensional Adaptive Quadrature

A working experimental program for n-dimensional adaptive quadrature is discussed. The program uses the simplex rather than the cube as the basic ''cell.'' Symmetric interpolatory quadratures of variable order are derived during execution and used as basic integrators. Integrand values are stored into a table by means of a double hashing technique for efficient retrieval. Iterated calls are allowed with the dimension of the region factored arbitrarily. Restarting the calculation for greater precision costs no more than if the user had requested the higher accuracy in the first place. 2 figures.

Mark B. Wells | David K. Kahaner | M. Wells | D. Kahaner

[1] L. Shapley. On Balanced Games Without Side Payments , 1973 .

[2] Mark B. Wells. Implementation and application of a function data type , 1977, AFIPS '77.

[3] A. Genz. An adaptive multidimensional quadrature procedure , 1972 .

[4] John R. Rice,et al. A Metalgorithm for Adaptive Quadrature , 1975, JACM.

[5] P. Silvester,et al. Symmetric Quadrature Formulae for Simplexes , 1970 .

[6] J. N. Lyness,et al. An error functional expansion for $N$-dimensional quadrature with an integrand function singular at a point , 1976 .

[7] J. N. Lyness. Quadrature over a Simplex: Part 2. A Representation for the Error Functional , 1978 .

[8] William H. Burge,et al. Recursive Programming Techniques , 1975 .

[9] R. Bruce Simpson,et al. Local Versus Global Strategies for Adaptive Quadrature , 1975, TOMS.

[10] C. D. Boor,et al. CADRE: AN ALGORITHM FOR NUMERICAL QUADRATURE , 1971 .

[11] J. N. Lyness. Quadrature over a Simplex: Part 1. A Representation for the Integrand Function , 1978 .

[12] Mark B. Wells,et al. The specification of program flow in Madcap 6 , 1972, SIGP.

[13] H. Kuhn. Simplicial approximation of fixed points. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[14] David K. Kahaner,et al. Double Integration Using One-Dimensional Adaptive Quadrature Routines: A Software Interface Problem , 1981, TOMS.