Abstract
In §4.6 several tensor operations have been described. The numerical tensor calculus requires the practical realisation of these operations. In this chapter we describe the performance and arithmetical cost of the operations for the different formats. The discussed operations are the addition in Sect. 13.1, evaluation of tensor entries in Sect. 13.2, the scalar product and partial scalar product in Sect. 13.3, the change of bases in Sect. 13.4, general binary operations in Sect. 13.5, Hadamard product in Sect. 13.6, convolution of tensors in Sect. 13.7, matrix-matrix multiplication in Sect. 13.8, and matrix-vector multiplication in Sect. 13.9. Section 13.10 is devoted to special functions applied to tensors. In the last Sect. 13.11 we comment on the operations required for the treatment of Hartree-Fock and Kohn-Sham applications in quantum chemistry.
In connection with the tensorisation discussed in Chap. 14, further operations and their cost will be discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag GmbH Berlin Heidelberg
About this chapter
Cite this chapter
Hackbusch, W. (2012). Tensor Operations. In: Tensor Spaces and Numerical Tensor Calculus. Springer Series in Computational Mathematics, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28027-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-28027-6_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28026-9
Online ISBN: 978-3-642-28027-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)