On the domain of divergence of Hermite-Fejer interpolating polynomials

[摘要] Recently, the study of the behavior of the Hermite-Fejer 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-Fejer interpolation to f(z) = z diverges everywhere in the complex plane outside the interval of inter polation [-1, 1]. In this note we amplify this result and prove that the divergence phenomenon takes place without any restriction on the interpolatory matrices. (C) 2000 Academic Press.

[发布日期] 2000-10-01

[关键词] Hermite-Fejer interpolation;divergence