The tensor t‐function: A definition for functions of third‐order tensors

Lund, Kathryn

doi:10.1002/nla.2288

Title: The tensor t‐function: A definition for functions of third‐order tensors

Journal Article · 20 February 2020 · Numerical Linear Algebra with Applications

DOI: https://doi.org/10.1002/nla.2288 · OSTI ID:1600869

^[1]

Charles University Prague Czech Republic

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.

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Sponsoring Organization:: USDOE

OSTI ID:: 1600869

Journal Information:: Numerical Linear Algebra with Applications, Journal Name: Numerical Linear Algebra with Applications Journal Issue: 3 Vol. 27; ISSN 1070-5325

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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