Polynomial approximation errors for functions of low-order continuity |
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| Authors: | David Elliott Peter J Taylor |
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| Institution: | 1. Department of Mathematics, University of Tasmania, G.P.O. Box 252C, 7001, Hobart, Tasmania, Australia
2. Department of Mathematics, University of Strathclyde, Glasgow, Scotland
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| Abstract: | Given a functionf defined on -1, 1] we obtain, in terms of (n+1)st divided differences, expressions for the minimax errorE n(f) and the errorS n(f) obtained by truncating the Chebyshev series off aftern+1 terms. The advantage of using divided differences is thatf is required to have no more than a continuous second derivative on -1, 1]. |
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