School of Mathematics

Convergence of the Magnus expansion

Per Christian Moan and Jitse Niesen.
"Convergence of the Magnus expansion".
J. Found. of Comp. Math., 8(3):291–301, 2008; doi:10.1007/s10208-007-9010-0; arXiv:math.CA/0609198.
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Abstract

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.