{"product_id":"tensor-numerical-methods-in-quantum-chemistry-9783110370157","title":"Tensor Numerical Methods in Quantum Chemistry","description":"\u003cp\u003eThe 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. \u003c\/p\u003e \u003cul\u003e \u003cli\u003eComputation 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\u003csup\u003e15\u003c\/sup\u003e. \u003c\/li\u003e \u003cli\u003eFast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. \u003c\/li\u003e \u003cli\u003eTensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. \u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003eThis research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing. \u003c\/p\u003e","brand":"Venera Khoromskaia","offers":[{"title":"Default Title","offer_id":48260905730299,"sku":"9783110370157","price":210.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0779\/3917\/9771\/files\/CoreSourceHub_71518595-5440-460c-ade3-f0cd38c2b029.jpg?v=1778451413","url":"https:\/\/indiepubs.com\/products\/tensor-numerical-methods-in-quantum-chemistry-9783110370157","provider":"IndiePubs","version":"1.0","type":"link"}