Comparison of algorithms for multivariate rational approximation
HTML articles powered by AMS MathViewer
- by Jackson N. Henry PDF
- Math. Comp. 31 (1977), 485-494 Request permission
Abstract:
Let F be a continuous real-valued function defined on the unit square $[ - 1,1] \times [ - 1,1]$. When developing the rational product approximation to F, a certain type of discontinuity may arise. We develop a variation of a known technique to overcome this discontinuity so that the approximation can be programmed. Rational product approximations to F have been computed using both the second algorithm of Remez and the differential correction algorithm. A discussion of the differences in errors and computing time for each of these algorithms is presented and compared with the surface fit approximation also obtained using the differential correction algorithm.References
- J. A. Brown and M. S. Henry, Best Chebyshev composite approximation, SIAM J. Numer. Anal. 12 (1975), 336–344. MR 382946, DOI 10.1137/0712027
- Jackson N. Henry, Computation of rational product approximations, Internat. J. Numer. Methods Engrg. 10 (1976), no. 6, 1289–1298. MR 458797, DOI 10.1002/nme.1620100608
- M. S. Henry and J. A. Brown, Best rational product approximations of functions, J. Approximation Theory 9 (1973), 287–294. MR 493070, DOI 10.1016/0021-9045(73)90095-6
- M. S. Henry and J. A. Brown, Best rational product approximations of functions, J. Approximation Theory 9 (1973), 287–294. MR 493070, DOI 10.1016/0021-9045(73)90095-6
- E. H. Kaufman Jr. and G. D. Taylor, An application of linear programming to rational approximation, Rocky Mountain J. Math. 4 (1974), 371–373. MR 339454, DOI 10.1216/RMJ-1974-4-2-371
- E. H. Kaufman Jr. and G. D. Taylor, Uniform rational approximation of functions of several variables, Internat. J. Numer. Methods Engrg. 9 (1975), no. 2, 297–323. MR 454460, DOI 10.1002/nme.1620090204
- G. A. Watson, A multiple exchange algorithm for multivariate Chebyshev approximation, SIAM J. Numer. Anal. 12 (1975), 46–52. MR 373229, DOI 10.1137/0712004
- Stanley E. Weinstein, Approximations of functions of several variables: Product Chebychev approximations. I, J. Approximation Theory 2 (1969), 433–447. MR 254475, DOI 10.1016/0021-9045(69)90012-4
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 485-494
- MSC: Primary 65D15
- DOI: https://doi.org/10.1090/S0025-5718-1977-0445786-0
- MathSciNet review: 0445786