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 ref. del art�culo LU-9783110370157

Contactar al vendedor

Denunciar este art�culo

Detalles bibliogr�ficos

T�tulo: Tensor Numerical Methods in Quantum Chemistry
Editor: De Gruyter, DE
Fecha de publicaci�n: 2018
Idioma: Ingl�s
ISBN 10: 3110370158
ISBN 13: 9783110370157
Encuadernaci�n: Hardback
Edici�n: 1st.
Estado: New
Dimensiones: 6,69�pulgadas de ancho por 0,69 de alto por 9,61 de largo
Peso: 679 gramos

Acerca de

Sinopsis

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.

Acerca del autor

Venera Khoromskaia and Boris N. Khoromskij, Max-Planck-Institute for Mathematics in the Sciences, Leipzig, Germany.

"Sobre este t�tulo" puede pertenecer a otra edici�n de este libro.

Descripci�n de la librer�a

Ver la p�gina web de la librer�a

Informaci�n empresarial del vendedor

Rarewaves USA
10100 West Sample Road, Ste 101, Coral Springs, FL, 33065, U.S.A.

Condiciones de venta y env�o

Condiciones de venta

Derecho a cancelaci�n

Condiciones de env�o

Please note that we do not offer Priority shipping to any country.

We currently do not ship to the below countries:

Afghanistan
Bhutan
Brazil
Brunei Darussalam
Channel Islands
Chile
Israel
Lao
Mexico
Russian Federation
Saudi Arabia
South Africa
Yemen

Please do not attempt to place orders with any of these countries as a ship to address - they will be cancelled.

Tarifas de env�o de Estados Unidos de America a Espa�a

Tarifas de env�o de Estados Unidos de America a Espa�a
Cantidad del pedido	De 15 a 27 d�as h�biles	De 15 a 27 d�as h�biles
Primer art�culo	EUR 3.42	EUR 3.42

Los plazos de entrega los establecen los vendedores y var�an seg�n el transportista y la ubicaci�n. Los pedidos que pasan por la aduana pueden sufrir retrasos y los compradores son responsables de los aranceles o tarifas asociadas. Los vendedores pueden ponerse en contacto con usted en relaci�n con cargos adicionales para cubrir cualquier aumento en los costes de env�o de los art�culos.