A generalization of Jameson's method for Sylvester's matrix equation

Abstract

This article is based on the work of Jameson who, in 1968, produced a solution of Sylvester's matrix equation. Jameson's method applies only to the case of a uniquesolution. In 1993 the present author produced an improved version of Jameson's formula. Here it is proposed to update Jameson's method so as to provide allsolutions when the solution is not unique.