Tensor Numerical Methods in Scientific Computing (Radon Series on Computational and Applied Mathematics, 19) - Hardcover

Khoromskij, Boris N.

Hardcover

ISBN 10: 3110370131 ISBN 13: 9783110370133

Verlag: De Gruyter, 2018

Inhaltsangabe

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

Über diesen Titel

Über die Autorin bzw. den Autor

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

Details zur Ausgabe

• Verlag: De Gruyter
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 3110370131
• ISBN 13: 9783110370133
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 379
• Kontakt zum Hersteller: Walter de Gruyter GmbH; productsafety@degruyterbrill.com; ; Genthiner Straße 13; Berlin; 10785; Deutschland