{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-frechet-derivative-of-the-tensor-t","title":"The Fréchet derivative of the tensor t-function","arxiv_id":"2302.09687","date":"2023-02-19","proceeding":null,"authors":["Kathryn Lund","Marcel Schweitzer"],"abstract":"The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in [K. Lund, The tensor t-function: a definition for functions of third-order tensors, Numer. Linear Algebra Appl. 27 (3), e2288]. In this work, we investigate properties of the Fr\\'echet 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 \\texttt{t-Frechet} toolbox hosted at \\url{https://gitlab.com/katlund/t-frechet} illustrate properties of the t-function Fr\\'echet derivative, as well as the efficiency and accuracy of the proposed algorithms.","url_abs":"https://arxiv.org/abs/2302.09687v3","url_pdf":"https://arxiv.org/pdf/2302.09687v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-frechet-derivative-of-the-tensor-t","repo_url":"https://gitlab.com/katlund/t-frechet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}