1982 Reports

Average Case Optimal Algorithms in Hilbert Spaces

Wozniakowski, Henryk; Wasilkowski, Grzegorz W.

We study optimal algorithms and optimal information for an average case model. This is done for linear problems in a separable Hilbert space equipped with a probability measure. We show, in particular, that for any measure, an affine spline algorithm is optimal among affine algorithms. The affine spline algorithm is defined in terms of the correlation operator and the mean element of the measure. We provide a condition on the measure which guarantees that the affine spline algorithm is optimal among all algorithms. The problem of optimal information is also solved.