CONTINUED-FRACTION SOLUTION OF MATRIX EQUATION AX-XB=C

<正> The matrix equation AX-XB=C is quite well known and basic. It plays an important role in algebra and applied mathematics. This paper is an extension of the author's previous work. Using the continued fraction associated with A and B, one obtains a standard constructive formula of the solution X in an algebraic form. In contrast to other known results, it can simplify the numerical computation of X. When B=-A is asymptotically stable and C is a positive definite Hermitian matrix, the Hermitian form with the coefficient matrix X for a Liapunov function can be immediately decomposed as the sum of some nonnegative definite Hermitian forms by this formula.