Accounting for Round-Off Errors When Using Gradient Minimization Methods

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