DECOMPOSITION METHODS FOR SOLVING ONE-PARAMETRIC LINEAR MATRIX EQUATIONS WITH COMPLEX MATRICES
Keywords:
one-parameter linear matrix equation, decomposition, Kronecker product, analytical solution, differential transformations, matrix and vector discrete, hypermatrices and hypervectors, recursive computational procedures, numerical and analytical solutions, a model example.Abstract
Analytical and numerical-analytical methods for solving one-parametric linear matrix equations are proposed. The first method is practically suitable for solving simple tasks with small dimensions, while the second – for solving any problem with analytical elements and easily implemented by means of modern information technologies. In both cases, the methods of the linear matrix algebra with Kronecker products are used. In the case of the numerical- analytical method, the main mathematical apparatus are direct and inverse differential transformations. At using these transformations, the solution of the original continuous problem is reduced to solving the recurrent chain of some linear systems of algebraic equations. In the case of these equations, first the so called matrix discretes for solving the initial problem are determined, and after that, the continuous solution is restored. A model example at whose solving by the proposed decomposition numerical-analytical method, an exact Maclaurin analytical solution confirming the simplicity and high computational efficiency of the method is obtaind.
