COMPARATIVE ANALYSIS OF DECOMPOSITION METHODS FOR DETERMINING COMPLEX ONE-PARAMETER GENERALIZED INVERSE MOORE-PENROSE MATRICES

Abstract

A comparative analysis of software implementations of the numerical-analytical decomposition methods for determining complex one-parameter generalized inverse Moore-Penrose matrices is presented in order to reveal their computational characteristics. The numerical-analytical methods are based on previously developed analytical relations based on the 4 Moore-Penrose conditions, and also use differential Pukhov transformations as the main mathematical apparatus. Based on the mentioned computational methods, an application software package has been developed using modern means of information technologies, in particular, the Python programming language, the math module, NumPy, SymPy and PyQt libraries.

For each method the software implementations of numerical-analytical methods are compared by the dependence of the execution time on the number of matrix discretes, by the dependence of the execution time on the size of the input matrix, by the dependence of the memory used on the number of matrix discretes, by the dependence of the memory used on the size of the input matrix. It is shown that as the number of matrix discretes increases, the accuracy of determining the generalized inverse matrix increases, but more computational resources are consumed, in particular, the execution time and memory used by each method increases. In addition, the software implementation of numerical-analytical methods developed based on the 3rd and 4th Moore-Penrose conditions requires less time and a smaller amount of memory than the software implementation of numerical-analytical methods developed based on the 1st and 2nd Moore-Penrose conditions.