1985 Reports

Optimal Algorithm for Linear Problems with Gaussian Measures

Wasilkowski, Grzegorz W.

We study optimal algorithms for linear problems in two settings: the average case and the probabilistic case settings. We assume that the probability measure is Gaussian. This assumption enables us to consider a general class of error criteria. We prove that in both settings adaption does not help and a translated spline algorithm is optimal. We also devise optimal information under some additional assumptions concerning the error criterion.