D-analogue of an algorithm for determining single-parametric Drazin generalized inverse matrix based on matrix full rank factorization

Abstract

The urgency of the research is caused by the wide application of Drazin generalized inverse matrix in the theory of finite Markov chains, in solving linear shifting system of differential equations, difference equations, problems of optimal control of dynamic systems; in several aspects of automated control systems, etc. The main aim of the study is to develop an algorithm for finding matrix discretes of single-parametric Drazin generalized inverse matrix in the field of differential transformations and restoring the original using reverse D-transformations. The methods used in the study: theory of numerical Drazin pseudoinverse matrices, theory of generalized parametric inverse matrices, matrix full rank factorization, direct and reverse differential transformations, linear transformations of vector space, linear algebra, numerical calculations of matrix discretes using MATLAB ver. R2011b software package. The results: The paper introduces rather simple numerical-analytical method for determining Drazin single-parametric generalized inverse matrix which can be easily implemented by means of contemporary information technologies. The illustration of the method by a single sample example for determining a special case of Drazin generalized inverse matrix - group inverse matrix, proved its computational efficiency and low computational error ratio.

Keywords

• single-parametric Drazin generalized inverse matrix
• full rank factorization of the matrix
• differential transformations
• information technologies