ИСТИНА

One of the most efficient way of solving multidimensional ill-posed problems is using of parallel computing that helps us to process a huge amount of data. But the round-off errors that grow with increasing amount of computations can significantly affect the final result of calculations. In this work an approach that is able to take into account these errors and to construct sufficiently stable approximate solution of an ill-posed problem is discussed. Several recent results will be presented on the study of the main issue of this work. The project has been partially supported by RFBR, project No.~14-01-31201, and by the Supercomputing Center of Lomonosov Moscow State University.