The Fréchet derivative of the tensor t-function
Abstract
The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer Linear Algebra Appl 27(3):e2288). In this work, we investigate properties of the Fréchet derivative of the tensor t-function and derive algorithms for its efficient numerical computation. Applications in condition number estimation and nuclear norm minimization are explored. Numerical experiments implemented by the t-Frechet toolbox hosted at https://gitlab.com/katlund/t-frechet illustrate properties of the t-function Fréchet derivative, as well as the efficiency and accuracy of the proposed algorithms.
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© The Author(s) 2023.
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Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 16 June 2023
Accepted: 24 May 2023
Revision received: 22 May 2023
Received: 17 February 2023
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- Max Planck Institute for Dynamics of Complex Technical Systems (MPI Magdeburg) (2)
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