Apr. 6 ~ Apr. 12, 2017

- Boris N. Khoromskij, Max Planck Institute for Mathematics in Sciences, Leipzig, Germany
- Venera Khoromskaia, Max Planck Institute for Mathematics in Sciences, Leipzig, Germany

Room 601 & 602, Pao Yue-Kong Library, Minhang Campus, Shanghai Jiao Tong University

No registration fee. Participants should cover their own lodging and meals.

Date | Time | Title | Venue |
---|---|---|---|

Apr. 6 | 14:00 ~ 15:00 | Lecture 1. Approximation of bivariate functions by separation of variables. Matrix case. Lecture 1&2 | 601 |

15:00 ~ 16:00 | Lecture 2. Matrix SVD, EVD, Cholesky decompositions. FFT transform. Kronecker product. | 601 | |

16:00 ~ 17:00 | Lecture 3. Matrix factorizations, examples and exercises in Matlab (Cholesky, LU, QR, Kron).Lecture 3 | 601 | |

Apr. 7 | 14:00 ~ 15:00 | Lecture 4. Basic rank-structured tensor formats: canonical (CP), Tucker decompositions.Lecture 4&5 | 601 |

15:00 ~ 16:00 | Lecture 5. Approximation of multivariate functions by the canonical and Tucker tensors. | 601 | |

16:00 ~ 17:00 | Lecture 6. Algorithms for Tucker decomposition with Matlab examples. Canonical-to-Tucker algorithm.Lecture 6 | 601 | |

Apr. 10 | 09:00 ~ 10:00 | Lecture 7. Polynomial and Sinc approximation of multivariate functions. Separable approximation in analytic form via the Laplace transform.Lecture 7&8&9 | 601 |

10:00 ~ 11:00 | Lecture 8. Matrix product states (MPS, TT) decomposition. Quantized tensor approximation in log-complexity (QCan, QTT). Super-fast integration. | 601 | |

11:00 ~ 12:00 | Lecture 9. Exercises in Matlab on sinc- and QTT approximation of discretized functions. | 601 | |

Apr. 11 | 14:00 ~ 15:00 | Lecture 10. Operators in many dimensions. Superfast Laplacian inverse, QTT-FFT and convolution.Lecture 10&11 | 602 |

15:00 ~ 16:00 | Lecture 11. Multi-parametric (stochastic) PDEs. Preconditioning in many dimensions. | 602 | |

16:00 ~ 17:00 | Lecture 12. Calculation of 3D integral operators in 1D complexity. Fast Hartree-Fock solver. Excitation energies by the Bethe-Salpeter equation.Lecture 12 | 602 | |

Apr. 12 | 09:00 ~ 10:00 | Lecture 13. Time-dependent (parabolic) problems in d + 1 formulation. Example of chemical master equation.Lecture 13&14 | 601 |

10:00 ~ 11:00 | Lecture 14. Equations with oscillating coecients. Asymptotic homogenization. The Hartree-Fock on lattice structured compounds. | 601 | |

11:00 ~ 12:00 | Lecture 15. Super-fast summation of electrostatic potentials on nite lattices with defects. Range separated tensor formats and application to general many-particle systems.Lecture 15 | 601 |

- Recommended literature for getting the preliminary impression (plus some knowledge in numerical linear algebra and Matlab programing):
- B.N. Khoromskij. Introduction to tensor numerical methods in scientific computing. Lecture Notes, Preprint 06-2011, University of Zuerich, 2010.
- B.N. Khoromskij. Tensors-structured Numerical Methods in Scientific Computing: Survey on Recent Advances. Chemometr. Intell. Lab. Syst. 110 (2012), 1-19.
- Boris N. Khoromskij. Tensor Numerical Methods for High-dimensional PDEs: Basic Theory and Initial Applications. ESAIM: Proceedings and Surveys, January 2015, Vol. 48, p. 1-28. E-preprint arXiv:1408.4053, 2014.
- V. Khoromskaia and B.N. Khoromskij. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies. Phys. Chem. Chem. Phys., 17:31491 - 31509, 2015 (open access).
- T. G. Kolda and B. W. Bader. Tensor Decompositions and Applications. SIAM Rev. 51(3) (2009) 455–500.

- The slides for each of one-day lecture (3-hours lectures) will be distributed one day before the lecture day (say, slides for the first 3 lectures distribute on April 5th).
- Students will need Matlab for programming practices.