METHODS FOR SOLVING ONE-PARAMETRIC GENERALIZED CONJUGATED ANALOGES OF SYLVESTER TYPE A(t)•X(t)•D(t)+F(t)•X*(t)•B(t)=C(t) MATRIX EQUATIONS
Hree methods are proposed for solving generalized one-paramteric conjugated analogues of Sylvester type matrix equations: analytical, as well as sequential and parallel numerical-analytical methods. The mentioned methods are based on the newest operational method- the differential transformations of G. Ye. Pukhov. Despite the analytical method is limited in practical applications because of the functionals in its composition, however, it serves as a basis for developing sequential and parallel numerical-analytical methods. The concept of "cumulative conditions of unique solvability of the problem" is introduced: a) one condition of hyper regularity corresponds to one-parametric Kronecker matrix and four conditions of regularity of one-parametric matrices included in the mathematical model of the source problem (under the analytical method); b) one condition of hyper regularity corresponds to Kronecker matrix of the initial matrices' discretes and four conditions of regularity of the same matrices’ discretes (under the sequential numerical-analytical method); c) one condition of super regularity corresponding to Kronecker super matrix of initial matrices’ discretes and four conditions of regularity of the same matrices' discretes (under the parallel numerical-analytical method). A model example is considered, which is solved using the sequential numerical-analytical method and the exact Taylor solution of the problem is obtained. The proposed methods in a certain way fill the existing gap in the examined field and serve as a basis for creating corresponding modules of applications (in particular, in the MATLAB), which can be effectively realized in conducting computational experiments to solve this class of problems.