Lecturers

Prof. Dr. Christoph Schwab

Dr. Maksim Rakhuba

Coordinator

Fernando Henriquez

First Meeting on Thursday 22/02/18 at 15:15 in HG D 1.1

The Seminar will address recently developed, tensor-formatted numerical methods for the numerical solution of high-dimensional PDEs, Data-Compression, and of high-dimensional Dynamical Systems.

• Completed BSc exams in MATH or RW/CSE.

To earn seminar credits the student must:

• Prepare a 45 min presentation of the selected topic (Date and Time TBD).
• Prepare a written report ("Ausarbeitung") in Latex.

• Vladimir Kazeev, Ivan Oseledets, Maxim Rakhuba and Christoph Schwab. QTT-finite-element approximation for multiscale problems I: model problems in one dimension. Adv. Comput. Math. 43 (2017), no. 2, 411–442.
• Sergey Dolgov and Dmitry Savostyanov. Alternating minimal energy methods for linear systems in higher dimensions. SIAM J. Sci. Comput. 36.5 (2014), A2248-A2271. arXiv Report.
• Maxim Rakhuba and Ivan Oseledets. Grid-based electronic structure calculations: the tensor decomposition approach. J. Comput. Phys. 312 (2016), 19–30. arXiv Report.
• Phani Motamarri, Vikram Gavini, and Thomas Blesgen. Tucker-tensor algorithm for large-scale Kohn-Sham density functional theory calculations. Phys. Rev. B 93.12 (2016), 125104.
• Ivan Oseledets and Eugene Tyrtyshnikov. TT-cross approximation for multidimensional arrays. Linear Algebra Appl. 432.1 (2010), 70-88.
• Maxim Rakhuba and Ivan Oseledets. Fast multidimensional convolution in low-rank tensor formats via cross approximation. SIAM J. Sci. Comput. 37.2 (2015), A565-A582. arXiv Report.
• Anthony Nouy. Higher-order principal component analysis for the approximation of tensors in tree-based low rank formats. Technical report arXiv:1705.00880.
• Thomas Boiveau, Virginie Ehrlacher, Alexandre Ern and Anthony Nouy. Low-rank approximation of linear parabolic equations by space-time tensor Galerkin methods. Technical report arXiv:1712.07256.
• Ivan Oseledets. Tensor-Train Decomposition. SIAM J. Sci. Comput. 33 (2011), no. 5, 2295–2317.