Hybrid symbolic-numeric integration in multiple dimensions via tensor-product series. (English) Zbl 1360.65082
Kauers, Manuel (ed.), Proceedings of the 2005 international symposium on symbolic and algebraic computation, ISSAC’05, Beijing, China, July 24–27, 2005. New York, NY: ACM Press (ISBN 1-59593-095-7). 84-91 (2005).
Keywords:
Geddes series scheme; Geddes-Newton series expansions; approximation of functions; bilinear series; deconstruction/approximation/reconstruction technique (DART); multiple integration; splitting operator; symbolic-numeric algorithms; tensor productsReferences:
| [1] | J. Bernsten, T. O. Espelid, and A. C. Genz. Algorithm 698: DCUHRE - An Adaptive Multidimensional Integration Routine for a Vector of Integrals. ACM Transactions on Mathematical Software, 17:452-456, 1991. 10.1145/210232.210234 · Zbl 0900.65053 |
| [2] | O. A. Carvajal. A New Hybrid Symbolic-Numeric Method for Multiple Integration Based on Tensor-Product Series Approximations. Master’s thesis, Univ of Waterloo, Waterloo, ON, Canada, 2004. |
| [3] | F. W. Chapman. Generalized Orthogonal Series for Natural Tensor Product Interpolation. PhD thesis, Univ of Waterloo, Waterloo, ON, Canada, 2003. |
| [4] | W. Cheney and W. Light. A Course in Approximation Theory. The Brooks/Cole Series in Advanced Mathematics. Brooks/Cole Publishing Co., Pacific Grove, California, 2000. |
| [5] | K. O. Geddes. Numerical Integration in a Symbolic Context. In B. W. Char, editor, Proc of SYMSAC’86, pages 185-191, New York, 1986. ACM Press. 10.1145/32439.32476 |
| [6] | K. O. Geddes and G. J. Fee. Hybrid Symbolic-Numeric Integration in Maple. In P. Wang, editor, Proc of ISAAC’92, pages 36-41, New York, 1992. ACM Press. 10.1145/143242.143262 · Zbl 0977.65500 |
| [7] | A. C. Genz and A. A. Malik. An Adaptive Algorithm for Numerical Integration over an N-Dimensional Rectangular Region. Journal of Computational and Applied Mathematics, 6:295-302, 1980. · Zbl 0443.65009 |
| [8] | J. M. Hammersley and D. C. Handscomb. Monte Carlo Methods. Methuen, 1964. · Zbl 0121.35503 |
| [9] | T. X. He. Dimensionality Reducing Expansion of Multivariate Integration. Birkhaüser, 2001. · Zbl 1085.65025 |
| [10] | F. J. Hickernell. What Affects Accuracy of Quasi-Monte Carlo Quadrature? In H. Niederreiter and J. Spanier, editors, Monte Carlo and Quasi-Monte Carlo Methods, pages 16-55. Springer-Verlag, Berlin, 2000. · Zbl 0941.65025 |
| [11] | C. Lemieux and P. L’Ecuyer. On Selection Criteria for Lattice Rules and Other Quasi-Monte Carlo Point Sets. Mathematics and Computers in Simulation, 55(1-3):139-148, 2001. 10.1016/S0378-4754(00)00254-8 · Zbl 0981.65007 |
| [12] | I. H. Sloan and S. Joe. Lattice Methods for Multiple Integration. Oxford University Press, 1994. · Zbl 0855.65013 |
| [13] | A. H. Stroud. Approximate Calculation of Multiple Integrals. Prentice-Hall, 1971. · Zbl 0379.65013 |
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