A Magnus Expansion for the Equation $Y'= AY - YB^*$

Abstract

The subject matter of this paper is the representation of the solution of the linear differential equation $Y'= AY - YB, Y(0) = Y_0,$ in the form $Y(t) = e^{Ω(t)}Y_0$ and the representation of the function n as a generalization of the classical Magnus expansion. An immediate application is a new recursive algorithm for the derivation of the Baker-Campbell-Hausdorff formula and its symmetric generalisation.