Block methods of multidimensional-matrix data analysis

Abstract

The paper is devoted to the substantiation and the software implementation of the block method for the solving of the multidimensional-matrix problems. For this purpose, the notion of the cell is introduced as the ordered set of the multidimensional matrices. The two-dimensional block matrices are considered along with the cells as the multidimensional-matrix block constructions. It is shown that the multidimensional-matrix problem formulated in terms of the cells is transformed in the natural way to the block two-dimensional problem. As an application, the problem of the estimation of the coefficients of the multidimensional-matrix polynomial regression function is considered. This problem is reduced to the numerical solution of the system of the multidimensional-matrix linear algebraic equations. The two methods to the solution of the system are developed: the block Gauss method and the block method of the matrix inverse. Both of them are realized programmatically as standard functions.