Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors

The paper proposes a parallel algorithm for solving large overdetermined systems of linear algebraic equations with dense matrix. This is based on the use modification conjugate gradient method, which able to take into account rounding errors accumulated during calculations when making decision terminate iterative process. constructed in such way that it takes capabilities message passing interface (MPI) programming technology, used software implementation proposed algorithm. examples are shown using Python language and mpi4py package, but all programs built they can be easily rewritten C/C++/Fortran languages. advantage modern MPI-4.0 standard demonstrated.