Approximation by Polynomials with Locally Geometric Rates
Copyright policy )Approximation by Polynomials with Locally Geometric Rates
In contrast to the behavior of best uniform polynomial approximants on [ 0 , 1 ] [0,1] we show that if f ∈ C [ 0 , 1 ] f \in C[0,1] there exists a sequence of polynomials { P n } \{ {P_n}\} of respective degree ≤ n \leq n which converges uniformly to f f on [ 0 , 1 ] [0,1] and geometrically fast at each point of [ 0 , 1 ] [0,1] where f f is analytic. Moreover we describe the best possible rates of convergence at all regular points for such a sequence.
- Florida Southern College United States
- Institute of Mathematics and Informatics Bulgaria
- Bulgarian Academy of Sciences Bulgaria
Approximation by polynomials, algebraic polynomials, Rate of convergence, degree of approximation, rates of convergence, best uniform polynomial approximants
Approximation by polynomials, algebraic polynomials, Rate of convergence, degree of approximation, rates of convergence, best uniform polynomial approximants
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