Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

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 ...

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...

On Solving Linear Diophantine Systems Using Generalized Rosser's Algorithm

Efficient implementation of stable Richardson Extrapolation algorithms

Richardson Extrapolation is a powerful computational tool which can successfully be used in the efforts to improve the accuracy of the approximate solutions of systems of ordinary differential equations (ODEs) obtained by different numerical methods (including here combined numerical methods consisting of appropriately chosen splitting procedures and classical numerical methods). Some stability...

Factors of Safety for Richardson Extrapolation

A factor of safety method for quantitative estimates of grid-spacing and time-step uncertainties for solution verification is developed. It removes the two deficiencies of the grid convergence index and correction factor methods, namely, unreasonably small uncertainty when the estimated order of accuracy using the Richardson extrapolation method is greater than the theoretical order of accuracy...