Lagrange interpolation and quadrature formula in rational systems

JOURNAL OF APPROXIMATION THEORY

卷:95

Article

Min, G

关键词: Lagrange interpolation;    rational system;    Lebesgue constant;    quadrature formula;    Chebyshev polynomials;   

DOI  :  10.1006/jath.1997.3214

来源: Elsevier

【 摘 要 】

This paper considers Lagrange interpolation in the rational system {1/(x - a(1)), 1/(x - a(2)), ...}, which is based on the zeros of the Chebyshev polynomial for the rational system {1, 1/(x - a(1)), 1/(x - a(2)), ...} with distinct real poles {a(k)}(k = 1)(infinity) subset of R\[ -1, 1]. The corresponding Lebesgue constant is estimated, and is shown to be asymptotically of order In n when the poles stay outside an interval which contains [ - 1, 1] in its interior. Some well-known results of classical polynomial interpolation are extended. (C) 1998 Academic Press.

【 授权许可】

Free