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Interpolatory Pointwise Estimates for Polynomial Approximation |
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| Authors: | H. H. Gonska D. Leviatan I. A. Shevchuk H. -J. Wenz |
| Affiliation: | Fachbereich Mathematik gonska@informatik.uni-duisburg.de, Universit?t Duisburg 47048 Duisburg Germany, DE School of Mathematical Sciences Israel leviatan@math.tau.ac.il, Sackler Faculty of Exact Sciences Tel Aviv University Tel Aviv 69978, IL Faculty of Mathematics and Mechanics shevchuk@imath.kiev.ua, National Taras Shevchenko University of Kyiv 252017 Kyiv Ukraine, UA Fachbereich Mathematik, wenz@informatik.uni-duisburg.de, Universit?t Duisburg 47048 Duisburg Germany, DE |
| Abstract: | We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f∈ C[0,1] , by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases. November 16, 1998. Date revised: July 12, 1999. Date accepted: September 13, 1999. |
| Keywords: | . Approximation by polynomials Shape-preserving approximation Degree of approximation Interpolatory pointwise estimates. AMS Classification. 41A10 41A25 41A29. |
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