Comparison of algorithms for multivariate rational approximation

Henry, Jackson N.

doi:10.1090/S0025-5718-1977-0445786-0

Comparison of algorithms for multivariate rational approximation
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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.

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