ONE GRADIENT DESCENT METHOD WITH ADAPTED STEP CORRECTION FOR SOLVING ARBITRARY SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS

The given paper continues and modifies results of [8], [12] and presents results of work of software product, written in «Visual Basic for Applications», designed for solving various systems of abstract linear algebraic equations. The product is based on optimization descent methods and classical Gauss methods with reduction of arbitrary matrix to triangular form. Developed with the help of synthesis both, classical and optimization, methods, this program is focused on solving an arbitrary system of linear algebraic equations with one unique solution or even infinite number of solutions, and, in the case of absence of some solution, the program calculates so-called discrepancy minimizer.