Estimates of Lebesgue constants for Lagrange interpolation processes by rational functions under mild restrictions to their fixed poles. (English) Zbl 1532.30010
The authors study the Lagrange interpolation problem on one or several intervals by rational functions with fixed poles. They summarize some of the main important known results of one of the authors an other authors on the estimation of the Lebesgue constants when the location of the poles of the rational approximants are located “not too close” to the interpolation interval. The main purpose of this paper is to generalize those results and let poles “closer” to the interpolation interval. More precisely, to estimate the Lebesgue constants when the poles of the rational approximants have finitely many accumulation points on the interpolation interval. By using an analog of the inverse polynomial image method for rational functions with fixed poles they show that the estimates previously obtained for the more restrictive situations analyzed in the mentioned known results, are also valid in the more general situation analyzed in this paper.
Reviewer: José L. Lopez (Pamplona)
MSC:
| 30E05 | Moment problems and interpolation problems in the complex plane |
| 30E10 | Approximation in the complex plane |
Software:
Algorithm 882References:
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