© 2012

Tensor Spaces and Numerical Tensor Calculus


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

About this book


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.


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

Authors and affiliations

  1. 1.for Mathematics in the SciencesMax-Planck-InstituteLeipzigGermany

About the authors

The author is working in the field of numerical mathematics for partial differential equations and integral equations. He has published monographs, e.g., about the multi-grid method, about the numerical analysis of elliptic pdes, about iterative solution of large systems of equation, and about the technique of hierarchical matrices.

Bibliographic information

Industry Sectors
Energy, Utilities & Environment


“The present book Tensor spaces and numerical tensor calculus by Wolfgang Hackbusch to a large extent fills the gap between theory on finite-dimensional tensor spaces and tensor computations. It also gives a comprehensive overview of numerical tensor computations. … the book is most useful as a (very rich) source book for researchers in the area. It might also be used as a textbook for a Ph.D. course … .” (Lars Eldén, Mathematical Reviews, October, 2015)