Iterated Bernstein polynomial approximations
نویسنده
چکیده
Iterated Bernstein polynomial approximations of degree n for continuous function which also use the values of the function at i/n, i = 0, 1, . . . , n, are proposed. The rate of convergence of the classic Bernstein polynomial approximations is significantly improved by the iterated Bernstein polynomial approximations without increasing the degree of the polynomials. The same idea applies to the q-Bernstein polynomials and the Szasz-Mirakyan approximation. The application to numerical integral approximations is also discussed. MSC: 41A10; 41A17; 41A25.
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