Parallel computing methods to determine parametric generalized inverse matrices

The relevancy of the work is conditioned by the necessity to determine effectively the Moore-Penrose generalized parametric inverse matrices which are quite often encountered when solving non-autonomous linear systems of finite equations, optimal control problems, non-autonomous matrix equations, singular decomposition problems, linear dynamic system splitting problems, linear multipoint boundary value problems, continuous tasks of mathematical programming problems, when finding out the roots of algebraic polynomials with variable coefficients. Work objective is to develop matrix-vector and array computational methods for determining Moore-Penrose generalized parametric inverse matrices.Methods of research: when solving the problem in question the following methods were used: linear algebra methods, matrix theory, differential transformation theory, numerical technique theory, parallel computing theory, computer modeling methods and data engineering. Results: The author has proved the theorem of determining the generalized parametric inverse matrices based on application of the differential transformation apparatus, reducing the solution of the continuous task to solution of the equivalent numeric problem providing high effectiveness of computational procedures.