LAGRANGE INTERPOLATION AND QUADRATURE FORMULA IN RATIONAL SYSTEMS

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 Che byshev 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 sho wn to be asymptotically of order In n when the poles stay outside an i nterval which contains [ - 1, 1] in its interior. Some well-known resu lts of classical polynomial interpolation are extended. (C) 1998 Acade mic Press.