The Fréchet derivative of the tensor t-function

The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, t-function: definition for Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties Fr\'echet derivative t-function and derive algorithms its efficient numerical computation. Applications condition number estimation nuclear norm minimization are explored. Numerical experiments implemented by \texttt{t-Frechet} toolbox hosted at \url{https://gitlab.com/katlund/t-frechet} illustrate derivative, as well efficiency accuracy proposed algorithms.