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Tensor Numerical Methods in Quantum Chemistry: Basic Algorithms and Applications - Couverture rigide
Synopsis
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.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Venera Khoromskaia and Boris N. Khoromskij, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Tensor Numerical Methods in Electronic Structure Calculations
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Venera Khoromskaia and Boris N. Khoromskij, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany. The conventional numerical methods when applied to multidimensional problems suffer from the . N° de réf. du vendeur 79663874
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Tensor Numerical Methods in Quantum Chemistry
Edité par
De Gruyter, De Gruyter, 2018
ISBN 10 : 3110370158
ISBN 13 : 9783110370157
Neuf
Couverture rigide
Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783110370157
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Tensor Numerical Methods in Quantum Chemistry
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De Gruyter, Mercury Learning And Information Aug 2024, 2024
ISBN 10 : 3110370158
ISBN 13 : 9783110370157
Neuf
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 298 pp. Englisch. N° de réf. du vendeur 9783110370157
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Tensor Numerical Methods in Quantum Chemistry
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Tensor Numerical Methods in Quantum Chemistry
Edité par
De Gruyter, De Gruyter Aug 2024, 2024
ISBN 10 : 3110370158
ISBN 13 : 9783110370157
Neuf
Couverture rigide
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -When applied to multidimensional problems, conventional numerical methods suffer from the so-called ¿curse of dimensionality¿, which cannot be eliminated by parallel methods and high-performance computers. In this book, the authors explain basic tensor formats and algorithms, showing how Tucker tensor decompositions originating from chemometrics brought about a revolution when applied to problems of numerical analysis.Walter de Gruyter, Genthiner Straße 13, 10785 Berlin 298 pp. Englisch. N° de réf. du vendeur 9783110370157
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Tensor Numerical Methods in Quantum Chemistry
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Tensor Numerical Methods in Quantum Chemistry
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Tensor Numerical Methods in Quantum Chemistry
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Tensor Numerical Methods in Quantum Chemistry
Edité par
De Gruyter, DE, 2018
ISBN 10 : 3110370158
ISBN 13 : 9783110370157
Neuf
Couverture rigide
Edition originale
Vendeur : Rarewaves USA, OSWEGO, IL, Etats-Unis
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Hardback. Etat : New. 1st. 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. N° de réf. du vendeur LU-9783110370157
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Tensor Numerical Methods in Quantum Chemistry
Edité par
De Gruyter, DE, 2018
ISBN 10 : 3110370158
ISBN 13 : 9783110370157
Neuf
Couverture rigide
Edition originale
Vendeur : Rarewaves USA United, OSWEGO, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
Hardback. Etat : New. 1st. 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. N° de réf. du vendeur LU-9783110370157
Quantité disponible : Plus de 20 disponibles