The Elimination Problem in the Least Square Method for a System of Linear Algebraic Equations

Abstract

For an overdetermined system of linear algebraic equations, the elimination problem is considered, that is, the problem of calculating a given linear form of a solution of the system without calculating the solution itself. Importantly, this system can be inconsistent; thus, the solution obtained by the least square method is used, that is, the solution of the system is obtained after applying the first Gauss transformation. Under certain conditions, the value of the linear form does not depend on the choice of a solution of this system in the case of its nonunique solvability.