Über Birkhoff-Interpolation und Richardson-Extrapolation

Interpolation strategies in repeated Richardson extrapolation

We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson...

Multilevel Richardson-Romberg extrapolation

We propose and analyze a Multilevel Richardson-Romberg (ML2R) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pag07] and the variance control resulting from the stratification introduced in the Multilevel Monte Carlo (MLMC) method (see [Gil08, Hei01]). Thus, in standard frameworks like discretization schemes of diffusion proc...

Richardson Extrapolation and the Bootstrap

Simulation methods, in particular Efron's (1979) bootstrap, are being applied more and more widely in statistical inference. Given data, (X1,* ,Xn), distributed according to P belonging to a hypothesized model P the basic goal is to estimate the distribution Lp of a function Tn (X1, * *Xn,P). The bootstrap presupposes the existence of an estimate P (X1, Xn) and consists of estimating Lp by the ...

On Multivariate Birkhoff Rational Interpolation

Lower Bounds by Birkhoff Interpolation

In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree d such that the number of powers that are required in such a representation must be at least of order d. This is clearly optimal up to a constant factor. Previous lower bounds for this problem were only of order Ω( √...