The numerical solution of X = A_{1}X + XA_{2} + D, X(0) = C
Edward Joseph Davison · IEEE Transactions on Automatic Control · 1975
The numerical solution of the general matrix differential equation\dot{X} = A_{1}X + XA_{2} + D, X(0) = CforXis considered where A1and A2are stable matrices. The algorithm proposed requires only8n^{2}words of memory (for largen) and converges in approximately50n^{3} \mus where μ is the multiplication time of the digital computer, andn = \max(n_{1},n_{2})whereA_{1} \in R^{n_{1} \times n_{1}} , A_{2} \in R^{n_{2} \times n_{2}}. The algorithm is particularly suitable for systems wherenis large (e.g,n \gg 10).