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MiS Preprint

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

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


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.

MSC Codes:
65F30, 65F50, 65F35
Schrodinger equation, Hartree-Fock method, tensor-product approximation, Density functional theory, Schrödinger equation

Related publications

2010 Repository Open Access
Heinz-Jürgen Flad, Wolfgang Hackbusch, Boris N. Khoromskij and Reinhold Schneider

Concepts of data-sparse tensor-product approximation in many-particle modelling

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 / Vadim Olshevsky... (eds.)
Hackensack, NJ : World Scientific, 2010. - pp. 313-347