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Preprints, Working Papers, ... Year : 2022

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

Stefano Pozza
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Abstract

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.
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Dates and versions

hal-03597313 , version 1 (04-03-2022)

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