Convergence of the Magnus Series

The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals the fundamental solution of the differential equation. The question considered in this paper is: When does the series converge? The main result establishes a necessary condition for convergence, which improves on several earlier results.

• Type: Journal
• Year: 2008
• Where: FOCM
• Authors: Per Christian Moan, Jitse Niesen
• Keywords: FOCM 2006, FOCM 2008, Infinite Series, Magnus Series, Matrix Exponential