Tensor Numerical Methods in Scientific Computing

Boris N. Khoromskij

Published by De Gruyter 2018

Tensor Numerical Methods in Scientific Computing

Boris N. Khoromskij

Volume 19 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110365917

Overview
Contents

About this book

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

Tensor-structured numerical methods in scientific computing provide a powerful tool for efficient computations in higher dimensions
Various exercises are included in the book
Applications in Engineering and Quantum Many Body Physics

Author / Editor information

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

Topics

Frontmatter Publicly Available Download PDF	I
Contents Publicly Available Download PDF	V
1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2. Theory on separable approximation of multivariate functions Requires Authentication Unlicensed Licensed Download PDF	9
3. Multilinear algebra and nonlinear tensor approximation Requires Authentication Unlicensed Licensed Download PDF	70
4. Superfast computations via quantized tensor approximation Requires Authentication Unlicensed Licensed Download PDF	153
5. Tensor approach to multidimensional integrodifferential equations Requires Authentication Unlicensed Licensed Download PDF	216
Bibliography Requires Authentication Unlicensed Licensed Download PDF	349
Index Requires Authentication Unlicensed Licensed Download PDF	367

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in applied mathematics and scientific computing.
Pages
- Front matter: 10
- Main content: 369
Keywords: Wissenschaftliches Rechnen; Numerik; Tensormethoden

eBook

Published: June 11, 2018
ISBN: 9783110365917

Hardcover

Published: June 11, 2018
ISBN: 9783110370133