| On Newman-Type Rational Interpolation to |x| at the Adjusted Chebyshev Nodes of the Second Kind |
| Received:April 10, 2009 Revised:October 14, 2009 |
| Key Words:
Newman-type rational interpolation adjusting the Chebyshev roots of the second kind exact order of approximation.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10601065). |
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| Abstract: |
| Recently Brutman and Passow considered Newman-type rational interpolation to $|x|$ induced by arbitrary sets of symmetric nodes in $[-1,1]$ and gave the general estimation of the approximation error. By their methods, one could establish the exact order of approximation for some special nodes. In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval $[0,1]$ and then extending this set to $[-1,1]$ in a symmetric way. We show that in this case the exact order of approximation is $O(\frac{1}{n^2})$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.02.002 |
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