SOLUTION OF STEYN-TYPE A(t).XT (t).B(t)-X(t)=C(t) ONE-PARAMETRIC TRANSPOSED ANALOGUES OF MATRIX EQUATIONS
Keywords:
Steyn-type one-parametric transposed analogue of the matrix equation with square matrix coefficients, problem reduction, analytical method of solution, differen- tial transformations, sequential numerical-analytical solution method, , parallel numerical- analytical solution method, conditions for unique solvability of the problem, means of modern information technologies, a model example with square matrix-coefficients, the exact Taylor solution.Abstract
One-parametric transposed analogues of Steyn-type matrix equations with quadratic coefficient matrices are considered. Analytical, as well, as sequential and parallel numeri- cal-analytical methods based on G.E. Pukhov’s differential transformations are proposed. Although the analytical method is limited in practical applications and is useful for prob- lems with small matrices, and their simple elements, it serves as a basis for developing the sequential and parallel numerical-analytical methods. The presented methods, in a certain way, complement the existing gap in the field considered and are easy to implement by means of modern information technologies. Corresponding conditions of unique solvability of the problem are obtained for all the methods. A model example with square coefficient matrices is considered for whose solution the sequential numerical-analytical method has been used for which the exact Taylor solution is obtained. The presented methods can be easily transformed into corresponding analogues for solving similar one-parametric prob- lems with rectangular coefficient matrices. At the same time, these methods remain valid up to the corresponding one-parametric generalized inverse matrices, as well as their ma- trix discrepancies.
