Abstract
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 a (linear) spline algorithm is optimal among linear algorithms. The spline algorithm is defined in terms of the covariance operator of the measure. We provide a condition on the measure which guarantees that the spline algorithm is optimal among all algorithms. The problem of optimal information is also solved.
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