SUMMARY
We consider the one-parameter conjugated analogs of Sylvester type matrix equations. On the basis of simple transformations we obtainthe equivalent matrix equation containing only the unknown matrix which should be determined. Next, using the apparatus of Kroneckerproducts of matrices, the analytical solution of the problem was obtained, which is limited in practical applications, but serves as a basis for the development of numerical-analytical methods for solving the original problem. Serial and parallel numerical and analytical solution methods are proposed based on the differential transformations G. E. Pukhov. With sequential numerical-analytical method we operate with numeric recursive procedures in the first stage of the calculation, and analytical relations – in the second stage. In parallel numerical-analytical method we operate with linear hypersystem of numerical equations in the first stage of the calculation, and analytical relations – in the second stage. For all the methods the relevant conditions for the unique solvability of the problem were obtained. A model example was considered for which using numerical and analytical methods an exact solution of the Taylor was obtained. The proposed numerical-analytical techniques can be efficiently implemented by means of modern information technology.