Comparison of algorithms for multivariate rational approximation

Abstract

Let F be a continuous real-valued function defined on the unit square [ − 1 , 1 ] × [ − 1 , 1 ] [ - 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.