On Some Extremal Properties of Lagrange Interpolatory Polynomials |
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| Authors: | S P Sidorov |
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| Institution: | Department of Mechanics and Mathematics, Saratov State University, Astrakhanskaya 83, Saratov, 410060, Russiaf1 |
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| Abstract: | In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that , where
n is a set of the linear operators with finite rank n+1 defined on
−1,1], and where
n+1 denotes the set of polynomials p=∑i=0n+1aixi of degreen+1 such that an+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes
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| Keywords: | degree of approximation linear positive operators operators of class Sm linear width finite-dimensional property Lagrange interpolatory polynomial |
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