Derivative error bounds for Lagrange interpolation: An extension of Cauchy's bound for the error of Lagrange interpolation
نویسندگان
چکیده
منابع مشابه
A Hilbert transform representation of the error in Lagrange interpolation
Let Ln [f ] denote the Lagrange interpolation polynomial to a function f at the zeros of a polynomial Pn with distinct real zeros. We show that f − Ln [f ] = −PnHe [ H [f ] Pn ] , where H denotes the Hilbert transform, and He is an extension of it. We use this to prove convergence of Lagrange interpolation for certain functions analytic in (−1, 1) that are not assumed analytic in any ellipse wi...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1991
ISSN: 0021-9045
DOI: 10.1016/0021-9045(91)90015-3