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Newton Interpolation in Fejér and Chebyshev Points
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bernd Fischer Lothar Reichel, Lothar |
| Copyright Year | 2010 |
| Abstract | Let T be a Jordan curve in the complex plane, and let Í) be the compact set bounded by T. Let / denote a function analytic on O. We consider the approximation of / on fî by a polynomial p of degree less than n that interpolates / in n points on T. A convenient way to compute such a polynomial is provided by the Newton interpolation formula. This formula allows the addition of one interpolation point at a time until an interpolation polynomial p is obtained which approximates / sufficiently accurately. We choose the sets of interpolation points to be subsets of sets of Fejér points. The interpolation points are ordered using van der Corput's sequence, which ensures that p converges uniformly and maximally to / on f! as n increases. We show that p is fairly insensitive to perturbations of / if T is smooth and is scaled to have capacity one. If T is an interval, then the Fejér points become Chebyshev points. This special case is also considered. A further application of the interpolation scheme is the computation of an analytic continuation of / in the exterior of T. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/mcom/1989-53-187/S0025-5718-1989-0969487-3/S0025-5718-1989-0969487-3.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Approximation Chebyshev polynomials Computation Continuation Finite difference Interpolation Imputation Technique Newton polynomial Newton's method |
| Content Type | Text |
| Resource Type | Article |
