Известия Томского политехнического университета: Инжиниринг георесурсов (May 2019)
Methods for determining complex on-parametric generalized inverse matrices
Abstract
The relevance of the research is caused by the necessity of the efficient definition of complex one-parameter generalized inverse matrices of Moore and Penrouse, which are often used when solving various science and engineering problems, and for its special case, definition of real generalized inverse matrices which are widely used in different geo-informational systems. The main aim of the research is to develop the constructive analytical and numeric-analytical methods of determining complex one-parameter generalized inverse matrices of Moore and Penrouse. Methods of research. The author has applied the methods of linear algebra, methods of theory of matrices as well as the direct and reverse differential transformations of G.E. Pukhov, which differ from the well-known integral transformations in the fact that passing from the originals' domain to the domain of its representation is generally implemented on the basis of a more simple operation - differentiation (in comparison with the integration at integral transformations) and the reverse pass is implemented based on a simple operation - addition (in comparison with the integration at integral transformations). Results. The author proposed the constructive analytical and numeric-analytical methods to dermine complex one-parameter generalized inverse matrices of Moore and Penrouse The analytical methods are based on the proposed decomposition matrix-pattern presentations, whereas numeric-analytical methods are based on joint use of these presentations and differential transformations. When the analytical methods are in practice applicable for small size matrices discussions and their simple analytical elements, then numeric-analytical methods are applicable for general case. On the other hand, actually the solution of the initial continuous problem brings to the solution of some recurrent chain of a series of discreet problems with numerical solutions (at the first stage of computations), and then to restoration of the continuous problem solution of the continuous problem on their basis (at the second stage of computations). The mentioned circumstances define the simplicity of realization of numeric-analytical methods by implementation of the modern means of information technologies.
