Tensor Spaces and Numerical Tensor Calculus

  • Wolfgang Hackbusch

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 56)

Table of contents

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

    1. Front Matter
      Pages 1-2
    2. Wolfgang Hackbusch
      Pages 3-21
    3. Wolfgang Hackbusch
      Pages 23-47
    4. Wolfgang Hackbusch
      Pages 49-94
  3. Functional Analysis of Tensor Spaces

    1. Front Matter
      Pages 95-96
    2. Wolfgang Hackbusch
      Pages 97-181
    3. Wolfgang Hackbusch
      Pages 183-200
    4. Wolfgang Hackbusch
      Pages 201-229
  4. Numerical Treatment

    1. Front Matter
      Pages 231-232
    2. Wolfgang Hackbusch
      Pages 233-256
    3. Wolfgang Hackbusch
      Pages 257-295
    4. Wolfgang Hackbusch
      Pages 297-346
    5. Wolfgang Hackbusch
      Pages 347-385
    6. Wolfgang Hackbusch
      Pages 387-451
    7. Wolfgang Hackbusch
      Pages 453-472
    8. Wolfgang Hackbusch
      Pages 473-505
    9. Wolfgang Hackbusch
      Pages 507-540
    10. Wolfgang Hackbusch
      Pages 541-558
    11. Wolfgang Hackbusch
      Pages 571-584
  5. Back Matter
    Pages 585-605

About this book


Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd 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. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.


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

Authors and affiliations

  • Wolfgang Hackbusch
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

Bibliographic information

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