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Check in the VVZ for a current information. Students can either take the first half as a course for 5 credits, or the applicable at the same time. Lecture notes The lecture notes will grapu updated throughout the.

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Spectral sparsifiers generalize cut sparsifiers, and have found many applications in designing graph algorithms. We develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. In the graph setting, this leads to ultra-sparsifiers that have optimal behavior in expectation. The first seven weeks treat the most basic notions and results, while the remaining seven weeks are devoted to somewhat more advanced topics. Numerical Analysis II.