Exponential convergence of a linear rational interpolant between transformed Chebyshev points

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 Introduction Let f be a complex function defined on an interval I of the real axis and let x0, x1, . . . , xn be n + 1 distinct points of I, which we do not assume e...

Rational Interpolation at Chebyshev points

The Lanczos method and its variants can be used to solve eeciently the rational interpolation problem. In this paper we present a suitable fast modiication of a general look-ahed version of the Lanczos process in order to deal with polynomials expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for rational interpolation at Chebyshev points, that is, at the...

A Rational Spectral Collocation Method with Adaptively Transformed Chebyshev Grid Points

A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev points. The locations of the grid points are adapted to singularities of the underlying solution, and the locations of these singularities are appro...

Distribution of Rational Points: A Survey

Exponentially Convergent Linear Rational Interpolation between Equidistant (and Other) Points ?

In Ber-Mit] we have used rational functions with a xed denominator (i.e., independent of the interpolated function) to construct interpolating linear projections with slowly increasing Lebesgue constants for arbitrary interpolation points. Their drawback was the relatively slow convergence of the interpolant as the number of points increases. In the present work we demonstrate how the convergen...