Abstract
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.
Original language | English |
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Pages (from-to) | 727-749 |
Number of pages | 23 |
Journal | Rocky Mountain Journal of Mathematics |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - 1986 |
ASJC Scopus subject areas
- General Mathematics