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Rational Approximation to |<i>x</i>| at Logarithmic Nodes
Department of Mathematics, Hangzhou Normal University, Hangzhou, China
Department of Mathematics, Hangzhou Normal University, Hangzhou, China
Department of Mathematics, Hangzhou Normal University, Hangzhou, China
- 1 Department of Mathematics, Hangzhou Normal University, Hangzhou, China
- 2 Department of Mathematics, Hangzhou Normal University, Hangzhou, China
- 3 Department of Mathematics, Hangzhou Normal University, Hangzhou, China
Advances in Pure Mathematics·Volume 11 (2021)·Pages 19–26·Published 13 January 2021·DOI10.4236/apm.2021.111003
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Abstract
Based on a node group , the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is regarding to X . Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is . The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.
KeywordsNewman Type Rational OperatorLogarithmicNodesApproximation Order
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