Standard techniques for polynomial approximation of functions can be generalized to methods for approximation with rational functions. The Pade approximation is based on the same idea as the Taylor polynomial approximation. It turns out that it provides a good approximation only at a selected point and its close vicinity, and that approximations become worse when we move away from the selected point. In Chebyshev approximation we use a different basis of polynomials which are known to behave more uniformly. It turns out that this basis really leads to a more uniform approximation and that the errors along the interval are smaller than those observed in Pade approximation. In the end, the best uniform rational approximation is considered. Following the standard Remes algorithm for best uniform polynomial approximation, its adaptation for rational functions is introduced. Since this algorithm is quite uneconomical, another simplistic procedure is presented, which according to the performed computational experiments does not give optimal solutions but nevertheless provides another method for a good uniform approximation.
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