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 / V. Olshevsky ... (eds.)
Singapore [u. a.] : 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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Abstract:
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.