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Lecture 1: Some old and new results on Information-Based Complexity

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ASC - Approximation, sampling and compression in data science

We give a short introduction to IBC and present some basic
definitionsand a few results. The general question is: How many function values (or values of other functionals) of $f$ do we need to compute $S(f)$ up to an error $epsilon$? Here $S(f)$ could be the integral or the maximum of $f$.
In particular we study the question: Which problems are tractable? When do we have the curse of dimension?

In the second talk we discuss complexity results for
numerical integration.

In particular we present results for the star discrepancy,
the curse of dimension for $C^k$ functions, and results for randomized algorithms

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

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