Comparison of algorithms for multivariate rational approximation

Author:
Jackson N. Henry

Journal:
Math. Comp. **31** (1977), 485-494

MSC:
Primary 65D15

DOI:
https://doi.org/10.1090/S0025-5718-1977-0445786-0

MathSciNet review:
0445786

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let *F* be a continuous real-valued function defined on the unit square . 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.

**[1]**J. A. BROWN & M. S. HENRY, "Best Chebyshev composite approximation,"*SIAM J. Numer. Anal.*, v. 12, 1975, pp. 336-344. MR**52**#3828. MR**0382946 (52:3828)****[2]**J. N. HENRY, "Computation of rational product approximations,"*Internat. J. Numer. Methods Engrg.*, v. 10, 1976, pp. 1289-1298. MR**0458797 (56:16997)****[3]**M. S. HENRY & J. A. BROWN, "Best rational product approximations of functions,"*J. Approximation Theory*, v. 9, 1973, pp. 287-294. MR**0493070 (58:12108a)****[4]**M. S. HENRY & S. E. WEINSTEIN, "Best rational product approximations of functions. II," J.*Approximation Theory*, v. 12, 1974, pp. 6-22. MR**0493071 (58:12108b)****[5]**E. H. KAUFMAN, JR. & G. D. TAYLOR, "An application of linear programming to rational approximation,"*Rocky Mountain J. Math.*, v. 4, 1974, pp. 371-373. MR**49**#4213. MR**0339454 (49:4213)****[6]**E. H. KAUFMAN, JR. & G. D. TAYLOR, "Uniform rational approximation of functions of several variables,"*Internat. J. Numer. Methods Engrg.*, v. 9, 1975, pp. 297-323. MR**0454460 (56:12711)****[7]**G. A. WATSON, "A multiple exchange algorithm for multivariate Chebyshev approximation,"*SIAM J. Numer. Anal.*, v. 12, 1975, pp. 46-52. MR**51**#9430. MR**0373229 (51:9430)****[8]**S. E. WEINSTEIN, "Approximation of functions of several variables: Product Chebyshev approximations. I,"*J. Approximation Theory*, v. 2, 1969, pp. 433-447. MR**40**#7683. MR**0254475 (40:7683)**

Retrieve articles in *Mathematics of Computation*
with MSC:
65D15

Retrieve articles in all journals with MSC: 65D15

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0445786-0

Article copyright:
© Copyright 1977
American Mathematical Society