Jump to ContentJump to Main Navigation
Show Summary Details

Khoromskij, Boris N.

Tensor Numerical Methods in Scientific Computing

Series:Radon Series on Computational and Applied Mathematics 19

    129,95 € / $149.99 / £118.00*

    eBook (PDF)
    Publication Date:
    June 2018
    Copyright year:
    2018
    ISBN
    978-3-11-036591-7
    See all formats and pricing

    Overview

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

    Aims and Scope

    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

    x, 369 pages
    Language:
    English
    Type of Publication:
    Monograph
    Keyword(s):

    MARC record

    MARC record for eBook

    request permissions

    More ...

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

    Comments (0)

    Please log in or register to comment.
    Log in