SUMMARYLet F be a continuous real-valued function defined on [ -1, 13 x [ -1, 13. For purposes of simplifaction in some numerical processes, one may desire to have an approximation of the function F. We present a known method of approximation called the best rational product approximation. When developing this approximation to F, certain types of discontinuities may arise. We develop a slight variation of a known technique to overcome such discontinuities. With this modified technique, it is then possible to develop a computer program to compute the approximation of F. A brief discussion of this program is presented along with some of the results which we have obtained.
Abstract.Let F be a continuous real-valued function defined on the unit square [-1,11 x [-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.
Three algorithms are used to compute polynomial approximate solutions to initial value problems. One algorithm is based on the Roberts' minimal degree algorithm, whereas the other two algorithms utilize variants of the second algorithms of Remes. Our analysis indicates that the algorithm based on the Roberts' minimal degree algorithm is superior to the others considered.
Abstract.Let F be a continuous real-valued function defined on the unit square [-1,11 x [-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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