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Tensor Numerical Methods in Quantum Chemistry by Venera Khoromskaia; Boris N. Khoromskij is a nonfiction available to read on EtoBox.

What is Tensor Numerical Methods in Quantum Chemistry about?

<P>The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results　 from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. </P> <UL> <LI>Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 10<SUP>15</SUP>. </LI> <LI>Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron

Who reads Tensor Numerical Methods in Quantum Chemistry?

Author

Venera Khoromskaia; Boris N. Khoromskij

Publisher

de Gruyter GmbH, Walter

Published

2018

Language

EN

ISBN

9783110391374

Category

nonfiction

Subjects

Mathematics, Science, Chemistry