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Tensor Numerical Methods in Scientific Computing
Buch von Boris Khoromskij
Sprache: Englisch

168,95 €*

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Beschreibung
The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms.

This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green's and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients.

Contents
Theory on separable approximation of multivariate functions
Multilinear algebra and nonlinear tensor approximation
Superfast computations via quantized tensor approximation
Tensor approach to multidimensional integrodifferential equations

The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms.

This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green's and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients.

Contents
Theory on separable approximation of multivariate functions
Multilinear algebra and nonlinear tensor approximation
Superfast computations via quantized tensor approximation
Tensor approach to multidimensional integrodifferential equations

Details
Erscheinungsjahr: 2018
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: X
369 S.
ISBN-13: 9783110370133
ISBN-10: 3110370131
Sprache: Englisch
Autor: Khoromskij, Boris
Hersteller: De Gruyter
Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Strasse 13, D-10785 Berlin, productsafety@degruyterbrill.com
Maße: 23 x 176 x 245 mm
Von/Mit: Boris Khoromskij
Erscheinungsdatum: 11.06.2018
Gewicht: 0,754 kg
Artikel-ID: 111017294
Details
Erscheinungsjahr: 2018
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: X
369 S.
ISBN-13: 9783110370133
ISBN-10: 3110370131
Sprache: Englisch
Autor: Khoromskij, Boris
Hersteller: De Gruyter
Verantwortliche Person für die EU: Walter de Gruyter GmbH, De Gruyter GmbH, Genthiner Strasse 13, D-10785 Berlin, productsafety@degruyterbrill.com
Maße: 23 x 176 x 245 mm
Von/Mit: Boris Khoromskij
Erscheinungsdatum: 11.06.2018
Gewicht: 0,754 kg
Artikel-ID: 111017294
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