论文信息 - Exponential convergence of a linear rational interpolant between transformed Chebyshev points - 字舞流文

Exponential convergence of a linear rational interpolant between transformed Chebyshev points

In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions.

Jean-Paul Berrut | Richard Baltensperger | Benjamin Noël | Jean-Paul Berrut | R. Baltensperger | Benjamin Noël

[1] H. Schwarz. Numerical Analysis , 1989 .

[2] Herbert E. Salzer,et al. Lagrangian interpolation at the Chebyshev points xn, [ngr][equiv]cos([ngr][pgr]/n), [ngr]=0(1) n; some unnoted advantages , 1972, Comput. J..

[3] Dan Kosloff,et al. A modified Chebyshev pseudospectral method with an O(N –1 ) time step restriction , 1993 .

[4] T. J. Rivlin. The Chebyshev polynomials , 1974 .

[5] C. Schneider,et al. Some new aspects of rational interpolation , 1986 .

[6] Ludger Kaup,et al. Holomorphic Functions of Several Variables: An Introduction to the Fundamental Theory , 1983 .

[7] Peter Henrici,et al. Essentials of numerical analysis, with pocket calculator demonstrations , 1982 .

[8] H. Mittelmann,et al. Lebesgue constant minimizing linear rational interpolation of continuous functions over the interval , 1997 .

[9] Jean-Paul Berrut,et al. Barycentric formulae for cardinal (SINC-)interpolants , 1989 .

[10] Jean-Paul Berrut,et al. The errors in calculating the pseudospectral differentiation matrices for C̆ebys̆ev-Gauss-Lobatto points , 1999 .

[11] Jean-Paul Berrut,et al. Rational functions for guaranteed and experimentally well-conditioned global interpolation , 1988 .

[12] Ludger Kaup,et al. Holomorphic Functions of Several Variables , 1983 .