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Short Course on Tensor Numerical Methods in Scientific Computing
18. November 2019 / 12:00 - 6. December 2019 / 12:00
Prof. Dr. Boris Khoromskij with the assistance of Dr. Venera Khoromskaia is offering a short course on Tensor Numerical Methods in Scientific Computing at Trier University on behalf of the Research Training Group on Algorithmic Optimization.
The course will consist of several two hour lectures as follows:
Monday, 18 Nov 2019 12:00 – 14:00 E 52
Tuesday, 19 Nov 2019 10:00 – 12:00 E 45
Wednesday, 20 Nov 2019 14:00 – 16:00 HS 10
Thursday, 21 Nov 2019 14:00 – 16:00 E 10
Friday, 22 Nov 2019 10:00 – 12:00 E 44
Monday, 2 Dec 2019 12:00 – 14:00 E 52
Tuesday, 3 Dec 2019 10:00 – 12:00 E 45
Wednesday, 4 Dec 2019 14:00 – 16:00 HS 10
Thursday, 5 Dec 2019 12:00 – 14:00 E 10
Friday, 6 Dec 2019 10:00 – 12:00 E 44
Course Abstract:
Solution of multi-dimensional problems by traditional numerical methods suffer from the so-called “curse of dimensionality”, that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a “smart” rank-structured tensor representation of the multivariate functions and operators, thus reducing solution of multidimensional integral-differential equations to 1D calculations. We show how the canonical, Tucker, tensor train (TT), quantized-TT (QTT) and range-separated tensor approximations provide the way to solve the multi-dimensional equations on low-parametric rank-structured manifolds. We consider tensor methods for the elliptic optimal control problems, for elliptic PDEs with oscillating coefficients and for some quantum chemical models. Matlab exercises for the tensor decomposition algorithms will be provided.
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