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Optimal sampling for approximation on general domains

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ASCW03 - Approximation, sampling, and compression in high dimensional problems

We consider the approximation of an arbirary function in any dimension from point samples. Approximants are picked from given or adaptively chosen finite dimensional spaces. Various recent works reveal that optimal approximations can be constructed at minimal sampling budget by least-squares methods with particular sampling measures. In this talk, we discuss strategies to construct these measures and their samples in the adaptive context and in general non-tensor-product multivariate domains.

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

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