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Tensor Spaces and Numerical Tensor Calculus

  • Wolfgang Hackbusch

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 42)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. Algebraic Tensors

    1. Front Matter
      Pages 1-2
    2. Wolfgang Hackbusch
      Pages 3-20
    3. Wolfgang Hackbusch
      Pages 21-46
    4. Wolfgang Hackbusch
      Pages 47-84
  3. Functional Analysis of Tensor Spaces

    1. Front Matter
      Pages 85-86
    2. Wolfgang Hackbusch
      Pages 87-156
    3. Wolfgang Hackbusch
      Pages 157-172
    4. Wolfgang Hackbusch
      Pages 173-196
  4. Numerical Treatment

    1. Front Matter
      Pages 197-198
    2. Wolfgang Hackbusch
      Pages 199-216
    3. Wolfgang Hackbusch
      Pages 217-248
    4. Wolfgang Hackbusch
      Pages 249-280
    5. Wolfgang Hackbusch
      Pages 281-314
    6. Wolfgang Hackbusch
      Pages 315-370
    7. Wolfgang Hackbusch
      Pages 371-384
    8. Wolfgang Hackbusch
      Pages 385-416
    9. Wolfgang Hackbusch
      Pages 417-446
    10. Wolfgang Hackbusch
      Pages 447-462
    11. Wolfgang Hackbusch
      Pages 473-486
  5. Back Matter
    Pages 487-500

About this book

Introduction

Special numerical techniques are already needed to deal with nxn matrices for large n. Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail,
a particular tensor calculus is needed to treat such problems.
The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc.

Keywords

high-dimensional problems numerical tensor calculus tensor formats tensor spaces tensorization

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.for Mathematics in the SciencesMax-Planck-InstituteLeipzigGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-28027-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-28026-9
  • Online ISBN 978-3-642-28027-6
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site