On Divergence of Hermite—Fejér Interpolation to f(z)=z in the Complex Plane |
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| Authors: | L Brutman I Gopengauz |
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| Institution: | (1) Department of Computer Science University of Haifa Haifa 31905 Israel lev@mathsc2.haifa.ac.il, IL;(2) Department of Mathematics Moscow Institute of Steel and Alloys Moscow Russia gie@gopengauz.misa.ac.ru, RU |
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| Abstract: | We show 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] . This result is in striking contrast to the behavior of the Lagrange interpolating polynomials.
June 15, 1998. Date accepted: January 26, 1999. |
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| Keywords: | , Hermite—,Fejér interpolation, Divergence, AMS Classification, 41A05, 41A10, |
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