Artificial intelligence

Abstract: In order to compute the best Chebyshev (uniform) approximation for a given function by polynomial spline of degree n with r fixed knots it is proposed to apply, after an appropriate modification, an algorithm for approximating many-variables function by a generalized polynomial. In the algorithm a reduction to the linear programming problem with the main dual maximum-problem is used. Analysis of the numerical results showed that in most cases the modified algorithm has computed spline approximations more precisely than other known algorithms.

Keywords: polynomial spline, best Chebyshev approximation, algorithm, linear programming.

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