Nonlinear best Chebyshev approximations and splines
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abstract
Necessity of using parametric nonlinear expressions and splines arises due to of the fact that real physical processes can be described by a great amount of different analytical dependencies, which are not described by polynomials and rational expressions or splines built on their basis. General classic technique of finding the best Chebyshev approximation spreads also on nonlinear approximations. But such approximations are not always possible. In the paper there are some theorems, which show conditions for the function f (x) and the expression F(A, x) = F(ao, a1 - am; x) for which the best Chebyshev approximation can be realized. Also there is proved a theorem that shows the direction to investigation of the expression F(A, X) in order to establish the conditions of existence of the best Chebyshev approximation of chosen kind.
