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Widths of convex sets and the power of adaption and randomization

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DREW01 - Multivariate approximation, discretization, and sampling recovery

We present bounds between different widths of convex subsets of Banach spaces, including Gelfand, Kolmogorov and Bernstein widths.Using this, and some relations between widths and minimal errors, we obtain bounds on the maximal gain of adaptive and randomizedalgorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets.  We conclude with an overview of the new state of the art and a list of open problems.   

This talk is part of the Isaac Newton Institute Seminar Series series.

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Goldsmiths' 1 Lecture Theatre (0_017), Department of Materials Science and Metallurgy, 27 Charles Babbage Road, Cambridge. CB3 0FS Fisher Building, St Johns College Sedgwick Museum

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