Tensor Numerical Methods in Quantum Chemistry / / Venera Khoromskaia, Boris N. Khoromskij.
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" ra...
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Khoromskaia, Venera, author. aut http://id.loc.gov/vocabulary/relators/aut Tensor Numerical Methods in Quantum Chemistry / Venera Khoromskaia, Boris N. Khoromskij. Berlin ; Boston : De Gruyter, [2018] ©2018 1 online resource (VIII, 289 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Frontmatter -- Contents -- 1. Introduction -- 2. Rank-structured formats for multidimensional tensors -- 3. Rank-structured grid-based representations of functions in ℝd -- 4. Multiplicative tensor formats in ℝd -- 5. Multidimensional tensor-product convolution -- 6. Tensor decomposition for analytic potentials -- 7. The Hartree–Fock equation -- 8. Multilevel grid-based tensor-structured HF solver -- 9. Grid-based core Hamiltonian -- 10. Tensor factorization of grid-based two-electron integrals -- 11. Fast grid-based Hartree–Fock solver by factorized TEI -- 12. Calculation of excitation energies of molecules -- 13. Density of states for a class of rank-structured matrices -- 14. Tensor-based summation of long-range potentials on finite 3D lattices -- 15. Range-separated tensor format for many-particle systems -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. 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 1015. Fast 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. Tensor 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. This 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 30. Aug 2021) Calculus of tensors. Quantum chemistry. Tensor algebra. Tensornumerische Methoden. MATHEMATICS / Applied. bisacsh Khoromskij, Boris N., author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter DG Plus eBook-Package 2018 9783110719550 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English 9783110604252 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 9783110603255 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 English 9783110604191 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2018 9783110603194 ZDB-23-DMA EPUB 9783110391374 print 9783110370157 https://doi.org/10.1515/9783110365832 https://www.degruyter.com/isbn/9783110365832 Cover https://www.degruyter.com/cover/covers/9783110365832.jpg |
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Khoromskaia, Venera, Khoromskaia, Venera, Khoromskij, Boris N., |
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Khoromskaia, Venera, Khoromskaia, Venera, Khoromskij, Boris N., Tensor Numerical Methods in Quantum Chemistry / Frontmatter -- Contents -- 1. Introduction -- 2. Rank-structured formats for multidimensional tensors -- 3. Rank-structured grid-based representations of functions in ℝd -- 4. Multiplicative tensor formats in ℝd -- 5. Multidimensional tensor-product convolution -- 6. Tensor decomposition for analytic potentials -- 7. The Hartree–Fock equation -- 8. Multilevel grid-based tensor-structured HF solver -- 9. Grid-based core Hamiltonian -- 10. Tensor factorization of grid-based two-electron integrals -- 11. Fast grid-based Hartree–Fock solver by factorized TEI -- 12. Calculation of excitation energies of molecules -- 13. Density of states for a class of rank-structured matrices -- 14. Tensor-based summation of long-range potentials on finite 3D lattices -- 15. Range-separated tensor format for many-particle systems -- Bibliography -- Index |
author_facet |
Khoromskaia, Venera, Khoromskaia, Venera, Khoromskij, Boris N., Khoromskij, Boris N., Khoromskij, Boris N., |
author_variant |
v k vk v k vk b n k bn bnk |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Khoromskij, Boris N., Khoromskij, Boris N., |
author2_variant |
b n k bn bnk |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Khoromskaia, Venera, |
title |
Tensor Numerical Methods in Quantum Chemistry / |
title_full |
Tensor Numerical Methods in Quantum Chemistry / Venera Khoromskaia, Boris N. Khoromskij. |
title_fullStr |
Tensor Numerical Methods in Quantum Chemistry / Venera Khoromskaia, Boris N. Khoromskij. |
title_full_unstemmed |
Tensor Numerical Methods in Quantum Chemistry / Venera Khoromskaia, Boris N. Khoromskij. |
title_auth |
Tensor Numerical Methods in Quantum Chemistry / |
title_alt |
Frontmatter -- Contents -- 1. Introduction -- 2. Rank-structured formats for multidimensional tensors -- 3. Rank-structured grid-based representations of functions in ℝd -- 4. Multiplicative tensor formats in ℝd -- 5. Multidimensional tensor-product convolution -- 6. Tensor decomposition for analytic potentials -- 7. The Hartree–Fock equation -- 8. Multilevel grid-based tensor-structured HF solver -- 9. Grid-based core Hamiltonian -- 10. Tensor factorization of grid-based two-electron integrals -- 11. Fast grid-based Hartree–Fock solver by factorized TEI -- 12. Calculation of excitation energies of molecules -- 13. Density of states for a class of rank-structured matrices -- 14. Tensor-based summation of long-range potentials on finite 3D lattices -- 15. Range-separated tensor format for many-particle systems -- Bibliography -- Index |
title_new |
Tensor Numerical Methods in Quantum Chemistry / |
title_sort |
tensor numerical methods in quantum chemistry / |
publisher |
De Gruyter, |
publishDate |
2018 |
physical |
1 online resource (VIII, 289 p.) |
contents |
Frontmatter -- Contents -- 1. Introduction -- 2. Rank-structured formats for multidimensional tensors -- 3. Rank-structured grid-based representations of functions in ℝd -- 4. Multiplicative tensor formats in ℝd -- 5. Multidimensional tensor-product convolution -- 6. Tensor decomposition for analytic potentials -- 7. The Hartree–Fock equation -- 8. Multilevel grid-based tensor-structured HF solver -- 9. Grid-based core Hamiltonian -- 10. Tensor factorization of grid-based two-electron integrals -- 11. Fast grid-based Hartree–Fock solver by factorized TEI -- 12. Calculation of excitation energies of molecules -- 13. Density of states for a class of rank-structured matrices -- 14. Tensor-based summation of long-range potentials on finite 3D lattices -- 15. Range-separated tensor format for many-particle systems -- Bibliography -- Index |
isbn |
9783110365832 9783110719550 9783110604252 9783110603255 9783110604191 9783110603194 9783110391374 9783110370157 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA433 |
callnumber-sort |
QA 3433 K49 42018 |
url |
https://doi.org/10.1515/9783110365832 https://www.degruyter.com/isbn/9783110365832 https://www.degruyter.com/cover/covers/9783110365832.jpg |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.63 |
dewey-sort |
3515.63 |
dewey-raw |
515.63 |
dewey-search |
515.63 |
doi_str_mv |
10.1515/9783110365832 |
oclc_num |
1041994386 |
work_keys_str_mv |
AT khoromskaiavenera tensornumericalmethodsinquantumchemistry AT khoromskijborisn tensornumericalmethodsinquantumchemistry |
status_str |
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ids_txt_mv |
(DE-B1597)428238 (OCoLC)1041994386 |
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Tensor Numerical Methods in Quantum Chemistry / |
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