METHODS FOR SOLVING SYLVESTER TYPE A(t) . X(t) . D(t)+F(t) . XT(t) B(t)=C(t) GENERALIZED ONE-PARAMETRIC TRANSPOSED ANALOGUES OF MATRIX EQUATIONS

Abstract

Three methods for solving Sylvester type generalized one-parametric transposed analogues of matrix equations with squared matrix-coefficients are proposed: analytical, consecutive and parallel numerical-analytical methods based on G.E. Pukhov’s differential transformations. For all the proposed methods, the corresponding conditions of one-valued solvability have been obtained. Though the analytical method is limited to practical applications, it serves as a basis for development of consecutive and parallel numeric-analytical methods. The latter have such a composition which enables to implement those methods quite easily by using modern IT means. The proposed methods definitely fill the existing gap in the researched field. Besides, they are easily transformed to the corresponding analogues for solving such problems with rectangular matrix-coefficients. In that case, instead of ordinary functional or numerical inverse matrices, generalized functional or numerical inverse matrices are used which in general define the approximate solutions of the problems under consideration. The proposed methods, as special cases, embrace Sylvester, Stein, Lyapunov and other types of solution methods for generalized one-parametric matrix equations. A method with squared matrix-coefficients modeling sample is discussed for the solution of which, the consecutive numerical-analytical method has been used. In that case, Tailor’s precise solution has been obtained, thus displaying the computational productivity of the proposed methods.