This paper discusses a method for taking into account rounding errors when constructing a
stopping criterion for the iterative process in gradient minimization methods. The main aim of this
work was to develop methods for improving the quality of the solutions for real applied minimization
problems, which require significant amounts of calculations and, as a result, can be sensitive to the
accumulation of rounding errors. However, this paper demonstrates that the developed approach
can also be useful in solving computationally small problems. The main ideas of this work are
demonstrated using one of the possible implementations of the conjugate gradient method for
solving an overdetermined system of linear algebraic equations with a dense matrix.