Convergence of the Magnus series

Details Convergence of the Magnus series Convergence of the Magnus series

2006-09-07

arxiv.org/abs/math/0609198v2

J. Found. of Comp. Math., 8(3):291--301, 2008

Mathematics

Classical Analysis and ODEs

11 pages; v2: added justification for conjecture, minor clarifications and corrections

Scientific paper

10.1007/s10208-007-9010-0

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 sufficient condition for convergence, which improves on several earlier results.

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