Konyagin, S. V. 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 Cited in 1 Document MSC: 41A25 Rate of convergence, degree of approximation 41A10 Approximation by polynomials Keywords:approximation by polynomials; degree of approximation; error estimation Citations:Zbl 0493.41028 PDFBibTeX XMLCite \textit{S. V. Konyagin}, Math. Notes 48, No. 4, 1010--1017 (1990; Zbl 0716.41017); translation from Mat. Zametki 48, No. 4, 58--68 (1990) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.