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- Title
The tensor t‐function: A definition for functions of third‐order tensors.
- Authors
Lund, Kathryn
- Abstract
Summary: A definition for functions of multidimensional arrays is presented. The definition is valid for third‐order tensors in the tensor t‐product formalism, which regards third‐order tensors as block circulant matrices. The tensor function definition is shown to have similar properties as standard matrix function definitions in fundamental scenarios. To demonstrate the definition's potential in applications, the notion of network communicability is generalized to third‐order tensors and computed for a small‐scale example via block Krylov subspace methods for matrix functions. A complexity analysis for these methods in the context of tensors is also provided.
- Subjects
DEFINITIONS; CIRCULANT matrices; MATRIX functions; KRYLOV subspace
- Publication
Numerical Linear Algebra with Applications, 2020, Vol 27, Issue 3, p1
- ISSN
1070-5325
- Publication type
Article
- DOI
10.1002/nla.2288