Abstract
This is the second part of studies on multilinear problems devoted to the average case setting. The first part deals with the worst case setting and appeared as a separate paper. Assuming that the space of a multilinear problem is a Hilbert space, we show that the spline algorithms are optimal. We also prove that adaption does not help. For the Banach case, we show how to reduce the analysis of multilinear problems to linear subproblems. In particular, we prove that adaption can help by the factor of at most k for k-linear problems. Optimality properties of spline algorithms are established. We illustrate our analysis by an example of the bilinear integration problem.
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