Realization of uniform approximation by applying mean-square approximation

In the paper the polynomial mean-square approximation method was applied, where the applied criterion was the value of the maximum error of the obtained approximation. The value of this error depends on the number of approximation points within the range. By changing the number of points within the range, it can be noticed that the value of the maximum error has the minimum value for a particular value of L number of considered points. For a polynomial of N degree, the optimum number of equidistant points of approximation L and the maximum error of approximation are determined. The proposed method was compared with a uniform approximation method, namely the Chebyshev polynomial. The examples included in the paper show that the proposed method yields smaller values of the maximum error than Chebyshev polynomial.