Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4632927 | Applied Mathematics and Computation | 2009 | 7 Pages |
Abstract
A sufficient condition is given for a continuous power series f(x) on [0, 1] to be the uniform limit of its sequence Pnf of interpolating polynomials at n + 1 equally spaced nodes. The proof is based on expanding the Newton coefficients of Pnf in terms of Stirling numbers of the second kind and applying an Abel-like summation formula. Convergence rates of Pnf and of related coefficient sequences are estimated. Similar results follow for Bernstein polynomials and their derivatives.
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
James Guyker,