Description of Algorithms for Balancing Numerical Matrices and Their Division Into Hierarchical Levels According to Their Type and Complexity

Abstract

This article describes a set of algorithms for so-called balancing of numerical matrices, which were developed by the author. Each section consists of several algorithms that are divided into different levels. The order of these levels depended on the chronology of the creation of certain algorithms. Chronology also affected the complexity of these balancing algorithms, so it can be argued that the algorithms are described in order from the simplest level to the most complex. It is important to emphasize that the purpose of the article is to describe the actions on matrices that determine the balancing algorithm of a certain level, and practical application will be the next step.