27th Conference of the International Linear Algebra Society (ILAS 2026)

The Fréchet derivative of the tensor t-function

May 18, 2026, 3:45 PM

25m

McBryde Hall 113 (Virginia Tech)

Minisymposium Talk Numerical Linear Algebra in Machine Learning Numerical Linear Algebra in Machine Learning

Speaker

Kathryn Lund (STFC Scientific Computing)

Description

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.