ИСТИНА

A method for taking into account rounding errors when constructing stopping criterion for the iterative process in gradient minimization methods in solving ill-posed problems will be discussed. The main motivation of the talk is the development of methods for improving the quality of solving real applied inverse problems, the solution of which requires significant amounts of calculations and, as a result, can be sensitive to accumulating rounding errors. However, the talk will also demonstrate that the developed approach can also be useful in solving computationally small problems. The main ideas of the talk will be 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.