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Parametric approximation of piecewise analytic functions. (English. Russian original) Zbl 0716.41017

Math. Notes 48, No. 4, 1010-1017 (1990); translation from Mat. Zametki 48, No. 4, 58-68 (1990).
The paper concerns error estimation for parametric approximation of piecewise analytic functions. The author proves for the best parametric approximation of order n the estimate \(\epsilon_ n(f)=O(e^{-c.n/\ln n})\) where c is a constant. This result is an improvement on the result of G. L. Iliev [PLISKA, Stud. Math. Bulg. 1, 93-99 (1977; Zbl 0493.41028)].
Reviewer: K.Najzar

MSC:

41A25 Rate of convergence, degree of approximation
41A10 Approximation by polynomials

Citations:

Zbl 0493.41028
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References:

[1] B. Sendov, ?Certain questions in the theory of approximations of functions and sets in the Hausdorff metric,? Usp. Mat. Nauk,24, No. 5, 141-178 (1969). · Zbl 0184.09101
[2] B. Sendov, ?Parametric approximation,? Annuaire Univ. Sofia Fac. Math.,64, 237-247 (1969/1970).
[3] J. Szabados, ?On parametric approximation,? Acta Math. Acad. Sci. Hungar.,23, Nos. 3-4, 275-287 (1972). · Zbl 0253.41016 · doi:10.1007/BF01896946
[4] V. A. Popov and G. L. Iliev, ?Parametric approximation of piecewise analytic functions,? PLISKA Studia Math. Bulgar.,1, 72-78 (1977). · Zbl 0493.41027
[5] G. L. Iliev, ?An improvement of Sendov’s estimation for parametric approximation of partially analytic functions,? PLISKA Studia Math. Bulgar.,1, 93-99 (1977). · Zbl 0493.41028
[6] S. N. Bernshtein, Extremal Properties of Polynomials and the Best Approximation of Continuous Functions of One Real Variable [in Russian], ONTI NKTP SSSR, Moscow (1937).
[7] A. Zygmund, Trigonometric Series. Vol. II, Cambridge Univ. Press, Cambridge (1959). · Zbl 0085.05601
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