On the Domain of Divergence of Hermite–Fejér Interpolating Polynomials |
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Authors: | L Brutman I Gopengauz P Vrtesi |
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Institution: | Department of Computer Science, University of Haifa, Haifa, 31905, Israelf1;b Department of Mathematics, Moscow Institute of Steel and Alloys, Moscow, Russia;c Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences, H-1053, Budapest, Hungary |
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Abstract: | Recently, the study of the behavior of the Hermite–Fejér interpolants in the complex plane was initiated by L. Brutman and I. Gopengauz (1999, Constr. Approx.15, 611–617). It was shown that, for a broad class of interpolatory matrices on −1, 1], the sequence of polynomials induced by Hermite–Fejér interpolation to f(z)≡z diverges everywhere in the complex plane outside the interval of interpolation −1, 1]. In this note we amplify this result and prove that the divergence phenomenon takes place without any restriction on the interpolatory matrices. |
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Keywords: | Hermite– Fejé r interpolation divergence |
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