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Numerical View of Kiel

The interdisciplinary center of numerical simulation of the Christian-Albrechts-University of Kiel in cooperation with the GAMM Committee Efficient numerical methods for pdes organises the workshop

2nd Scientific Computing Seminar

Approximation in High Dimensions and the Electronic Schrödinger Equation

Christian-Albrechts-University of Kiel, Germany
June 29th to July 1st, 2006.
June/July 2006
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16.20 - 16.55 Boris Khoromskij ( (Leipzig):
Orthogonal Tucker tensor decomposition in many-particle modeling

Thursday
29.6.2006

The orthogonal Tucker tensor-decomposition of higher-order tensors can be applied to the classical potentials and to more complicated nonlocal operators arising in many-particle models. We are able to prove the exponential convergence in the Tucker rank for a wide class of function related tensors. The superconvergence of the Tucker decomposition with respect to the relative Frobenius norm is described. We show that the two-level Tucker model reduces the canonical approximation of the target tensor to a decomposition of the small-size core tensor.

Basic multi-linear algebra operations are performed with the asymptotically optimal cost.

We present numeriacal results for 3-th order tensors generated by the classical potentials

erf{|x|) / |x|,   1 / |x-y|,   e-α |x-y| and e-|x-y|/ |x-y|
with x,y ε Rd as well as for solutions of the Hartree-Fock and Ornstein-Zernike equations arising in the electron and molecular density function calculations. Numerical results illustrate almost exponential convergence in the Tucker rank and show robustness of the ALS iteration.

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