Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method
Classical Analysis and ODEs
2021-04-22 v3
Abstract
We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally establishes the convergence of the Lanczos-like algorithm and yields a full characterization of algorithmic breakdowns. From there, the solution of the original differential system is available in closed form. This is a key piece in evaluating the elusive ordered exponential function both formally and numerically.
Cite
@article{arxiv.2002.06973,
title = {Tridiagonalization of systems of coupled linear differential equations with variable coefficients by a Lanczos-like method},
author = {P. -L. Giscard and S. Pozza},
journal= {arXiv preprint arXiv:2002.06973},
year = {2021}
}