Preprint 3/2008

Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling

Heinz-Jürgen Flad, Wolfgang Hackbusch, Boris N. Khoromskij,and Reinhold Schneider

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Submission date: 10. Jan. 2008
Pages: 32
published in: Matrix methods : theory, algorithms and applications ; dedicated to the memory of Gene Golub ; based on the 2nd international conference on matrix methods and operator equations, Moscow, Russia, July 23-27, 2007 / V. Olshevsky ... (eds.)
Hackensack, NJ : World Scientific, 2010. - P. 313 - 347 
MSC-Numbers: 65F30, 65F50, 65F35
Keywords and phrases: Schrodinger equation, Hartree-Fock method, tensor-product approximation, Density functional theory, Schrödinger equation
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We present concepts of data-sparse tensor approximations to the functions and operators arising in many-particle models of quantum chemistry. Our approach is based on the systematic use of structured tensor-product representations where the low-dimensional components are represented in hierarchical or wavelet based matrix formats. The modern methods of tensor-product approximation in higher dimensions are discussed with the focus on analytically based approaches. We give numerical illustrations which confirm the efficiency of tensor decomposition techniques in electronic structure calculations.

07.10.2017, 01:41