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arXiv · 1909.03437

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

Pierre-Louis Giscard·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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BibTeXRIS

Pierre-Louis Giscard, Stefano Pozza. 2019-09-08. A Lanczos-like method for non-autonomous linear ordinary differential equations. https://doi.org/10.1007/s40574-022-00328-6

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