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 that a translated spline algorithm is optimal. We also derive optimal information under some additional assumptions concerning the error criterion.
|Number of pages||23|
|Journal||Rocky Mountain Journal of Mathematics|
|State||Published - 1986|
ASJC Scopus subject areas
- Mathematics (all)