{"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/exponential-time-differencing-for-matrix","title":"Exponential time differencing for matrix-valued dynamical systems","arxiv_id":"2406.13761","date":"2024-06-19","proceeding":null,"authors":["Nayef Shkeir","Tobias Schäfer","Tobias Grafke"],"abstract":"Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many cases, their tightest stability condition is coming from a linear term. Exponential time differencing (ETD) is known to produce highly stable numerical schemes by treating the linear term in an exact fashion. In particular, for stiff problems, ETD methods are a method of choice. We propose an extension of the class of ETD algorithms to matrix-valued dynamical equations. This allows us to produce highly efficient and stable integration schemes. We show their efficiency and applicability for a variety of real-world problems, from geophysical applications to dynamical problems in machine learning.","url_abs":"https://arxiv.org/abs/2406.13761v1","url_pdf":"https://arxiv.org/pdf/2406.13761v1.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":"abstracts"},"code_links":[{"paper_slug":"exponential-time-differencing-for-matrix","repo_url":"https://github.com/Nayef-S/Matrix_ETD","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","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}