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Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling
Heinz-Jürgen Flad, Wolfgang Hackbusch, Boris N. Khoromskij and Reinhold SchneiderAbstract
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.
- Received:
- 10.01.08
- Published:
- 10.01.08
- MSC Codes:
- 65F30, 65F50, 65F35
- Keywords:
- Schrodinger equation, Hartree-Fock method, tensor-product approximation, Density functional theory, Schrödinger equation
Related publications
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