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Tensor Numerical Methods in Scientific Computing

Boris N. Khoromskij (Autor)

Buch | Hardcover

X, 369 Seiten

2018
De Gruyter (Verlag)
978-3-11-037013-3 (ISBN)

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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

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

Erscheinungsdatum	11.06.2018
Reihe/Serie	Radon Series on Computational and Applied Mathematics ; 19
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	761 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Schlagworte	Numerik • Tensormethoden • wissenschaftliches Rechnen
ISBN-10	3-11-037013-1 / 3110370131
ISBN-13	978-3-11-037013-3 / 9783110370133
Zustand	Neuware