Tensors in computations
- 1 May 2021
- journal article
- research article
- Published by Cambridge University Press (CUP) in Acta Numerica
- Vol. 30, 555-764
- https://doi.org/10.1017/s0962492921000076
Abstract
The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way through the lens of linear algebra and numerical linear algebra, elucidated with examples from computational and applied mathematics.Keywords
This publication has 196 references indexed in Scilit:
- On the computational complexity of membership problems for the completely positive cone and its dualComputational Optimization and Applications, 2013
- Finding the Homology of Submanifolds with High Confidence from Random SamplesDiscrete & Computational Geometry, 2008
- Multilinear Calderón–Zygmund TheoryAdvances in Mathematics, 2002
- On the Hardness of Approximating the Chromatic NumberCombinatorica, 2000
- A unified approach to polynomially solvable cases of integer “non-separable” quadratic optimizationDiscrete Applied Mathematics, 1995
- On the second eigenvalue of hypergraphsCombinatorica, 1995
- Sums of even powers of real linear formsMemoirs of the American Mathematical Society, 1992
- O(n2.7799) complexity for n × n approximate matrix multiplicationInformation Processing Letters, 1979
- Produits tensoriels topologiques et espaces nucléairesMemoirs of the American Mathematical Society, 1955
- N herungsmethode zur L sung des quantenmechanischen Mehrk rperproblemsThe European Physical Journal A, 1930