D-ANALOGUE OF THE REGULARIZATION METHOD FOR DETERMINING ONE-PARAMETER GENERALIZED INVERSE MATRICES

Abstract

At present, world information technologies, in comparison with other areas, are showing the pace of permanent accelerated development, which makes it possible to apply completely new approaches in various areas of human activity to effectively solve the problems encountered in them.

One-parameter matrices, their inverse and generalized inverse matrices are quite often used in various scientific studies, applied problems, etc. However, the currently existing methods for their determination are usually effectively used only in special cases, and even they are difficult to implement from a practical point of view due to the need of performing a sufficiently large amount of computational operations.

The noted circumstances require the development of new, more efficient methods for solving the problems under consideration and achieving the best architecture of the developed tools. We hope that the present study serves this purpose to some extent. The advantage of the latter is that when it is applied, continuous (functional) problems are actually reduced to some sets of recurrent digital problems (at the first stage of calculations), which are easily amenable to solving by serial and parallel means of modern information technologies and restoring based on the obtained solutions of those digital problems of continuous solutions of initial continuous problems (at the second stage of calculations). These important circumstances are especially significant against the backdrop of current global trends in the widespread use of digital technologies in various fields of science and technology.

The basis of this study is the regularization method of A.Kh. Tikhonov. Further computational procedures are based on the latest operational method of G.E. Pukhov.