The algebraic polynomial interpolation on n+1 uniformly distributed nodes can be affected by the Runge phenomenon, also when the function f to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock- Chebyshev interpolation which produces a polynomial P that interpolates f on a subset of m+1 of the given nodes whose elements mimic as well as possible the Chebyshev–Lobatto points of order m. In this work we use the simultaneous approximation theory to produce a polynomialP of degree r, greater than m, which still interpolates f on the m + 1 mock-Chebyshev nodes minimizing, at the same time, the approximation error in a least-squares sense on the other points of the sampling grid. We give indications on how to select the degree r in order to obtain polynomial approximant good in the uniform norm. Furthermore, we provide a sufficient condition under which the accuracy of the mock-Chebyshev interpolation in the uniform norm is improved. Numerical results are provided.
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|Titolo:||On the constrained mock-Chebyshev least-squares|
|Data di pubblicazione:||2015|
|Citazione:||On the constrained mock-Chebyshev least-squares / De Marchi, S; Dell'Accio, Francesco; Mazza, M.. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 1879-1778. - 280(2015), pp. 94-109.|
|Appare nelle tipologie:||1.1 Articolo in rivista|