A Lanczos-like method for non autonomous linear ordinary differential equations

P.-L Giscard (1) , Stefano Pozza

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

The time-ordered exponential is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. In spite of being at the heart of much system dynamics, control theory, and model reduction problems, the time-ordered exponential function remains elusively difficult to evaluate. The *-Lanczos algorithm is a (symbolic) algorithm capable of evaluating it by producing a tridiagonalization of the original differential system. In this paper, we explain how the *-Lanczos algorithm is built from a generalization of Krylov subspaces, and we prove crucial properties, such as the matching moment property. A strategy for its numerical implementation is also outlined and will be subject of future investigation.

Mots clés: Lanczos algorithm; Matrix differential equations; Time-ordered exponential; Matching moments; Tridiagonal matrices; Ordinary differential equations

Domaines: Analyse classique [math.CA]; Analyse numérique [math.NA]; Systèmes dynamiques [math.DS]

P.-L Giscard, Stefano Pozza. A Lanczos-like method for non autonomous linear ordinary differential equations. 2022. ⟨hal-03597313⟩