ISSAC '97 Poster Abstracts.

We consider the following problem: suppose there exist numerical algorithms for obtaining the parameters of n best Chebyshev approximations by different expressions. F k ( A,x ) = F k ( a 0 , a 1 ,…, a m ; x ), k = 1,2,…, n. (1)to a function f ( x ) on an interval [ a, b ]. If the quantity ( m +1) of the unknown parameters is the same, then the proper choice of the form of approximating expression F k ( A,x ) can greatly reduce the maximum error of approximation [1,3]. The procedures for choosing the proper form of approximating expressions are not found in any computer algebra systems due to the great amount of calculations needed. All the more the approximations with different expressions on subintervals are not used. But the evaluation time can be impressively decreased by using analytical transformations.