Extrapolation quadrature from equispaced samples of functions with jumps

Impossibility of Approximating Analytic Functions from Equispaced Samples

It is shown that no stable procedure for approximating functions from equally spaced samples can converge geometrically for analytic functions. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992. In a nutshell, you can't beat Gibbs and Runge. Monday December 14 2009 4:30 PM Building 4, Room 370 Refreshments are available in Building 2, Room ...

Impossibility of Fast Stable Approximation of Analytic Functions from Equispaced Samples

It is shown that no stable procedure for approximating functions from equally spaced samples can converge exponentially for analytic functions. To avoid instability, one must settle for root-exponential convergence. The proof combines a Bernstein inequality of 1912 with an estimate due to Coppersmith and Rivlin in 1992.

Extrapolation-based Boundary Element Quadrature

Quadrature over Curved Surfaces by Extrapolation

In this paper we describe and justify a method for integrating over curved surfaces. This method does not require that the Jacobian be known explicitly. This is a natural extension of extrapolation (or Romberg integration) for planar squares or triangles.

Christoffel functions for weights with jumps∗

The asymptotic behavior of Christoffel functions is established at points of discontinuity of the first kind.