Sufficient conditions for the convergence of the Magnus expansion
- 28 November 2007
- journal article
- research article
- Published by IOP Publishing in Journal of Physics A: Mathematical and Theoretical
- Vol. 40 (50), 15001-15017
- https://doi.org/10.1088/1751-8113/40/50/006
Abstract
Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation Y'=A(t)Y. The first one provides a bound on the convergence domain based on the norm of the operator A(t). The second condition links the convergence of the expansion with the structure of the spectrum of Y(t), thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.Keywords
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