Tensor product approximation with optimal rank in quantum chemistry.

By Sambasiva Rao Chinnamsetty, M. Espig, Boris N. Khoromskij, Wolfgang Hackbusch, Heinz-Jürgen Flad. 2007

61 citations recorded by the source corpus.

Subfields: Computational Mathematics, Spectroscopy, Statistical and Nonlinear Physics

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “…convolution [152]; • computational tasks in electronic structure calculations, e.g., based on Hartree-Fock or DFT models [23,24,31,44,45,47,87,141–146,150,156–159]; • the solution of stochastic and parametric PDEs [68,69,76,77,161,165,171,189,202]; • approximation of Green’s…”
Efficient Analysis of High Dimensional Data in Tensor Formats (2012, background): “The similar splitting work, but in application in another context was done in [12, 13, 10, 11, 5].”
Efficient multi-scale computation of products of orbitals in electronic structure calculations (2010, methodology): “Within the present work, we focus on an alternative approach for the computation of two-electron integrals [11,12,31] which is based on the best fixed-rank tensor product approximation of orbitals.”
Concepts of Data-Sparse Tensor-Product Approximation in Many-Particle Modelling (2008, methodology): “Similar results for wavelets are presented in [14].”
Black Box Low Tensor-Rank Approximation Using Fiber-Crosses (2009, background): “Nonetheless, available state-of-the-art methods are quite efficient and have proven to be reliable in many practical cases [2, 4, 7].”
Use of tensor formats in elliptic eigenvalue problems (2012, unknown): “…E. Tyrtyshnikov 3 1Max-Planck-Institut für Mathematik in den Naturwissenschaften, D-04103, Leipzig, Germany 2Universität Zürich, Switzerland 3Institute of Numerical Mathematics, Russian Academy of Sciences, Gubkina 8, 119333 Moscow, Russia SUMMARY We investigate approximations to eigenfunctions…”
Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions (2013, unknown): “For ALS there is also a lack of convergence estimates both in the classical papers [16, 4], and in the recent ones, where ALS was applied to the Tucker model [5, 33], tensor trains [29], hierarchical Tucker format [25] and high–dimensional interpolation [34].”
Adaptive low rank wavelet methods and applications to two-electron Schrödinger equations (2012, background): “, in density fitting schemes in quantum chemistry – the combination of separable expansions with wavelet approximation of lower-dimensional factors has been considered in [25, 26, 24, 27].”
Regularity of Tensor Product Approximations to Square Integrable Functions (2011, background): “We ask the following question: Which regularity can we expect the factors uk of a best approximation to have in comparison to the regularity of f ? This question is important for instance in quantum chemistry [2,3,5, 9,10], where tensor products are used to approximate wave functions of atoms and mo”
A regularized Newton method for the efficient approximation of tensors represented in the canonical tensor format (2012, methodology): “In [4,5] we made the same observation as for the model problem.”
The tensor product approximation to single-electron systems (2009, methodology): “More details have already been discussed in our previous article [5] and also in [6].”