Vladimir S. Hybrid algorithms research and solving systems of linear algebraic equations with sparse matrices

Developed and researched hybrid algorithms for direct and iterative methods for solving systems of linear algebraic equations with sparse matrices arising in the mathematical modeling of processes and phenomena in different subject areas, which solving linear algebra is one of the stages. The ideological prerequisite for the use of hybrid computing in the processing of sparse matrices arbitrary structure are previous reordering sparse matrix to block-diagonal form with framing. Hybrid algorithms developed direct methods of investigation and solving SLE based on sparse Holesky factorization of the block-diagonal matrix with border and hybrid algorithms for single-step iterative methods for solving SLE based on triangular methods (Seidel, upper relaxation, alternately triangular method) for sparse block-diagonal matrix with border. The properties of hybrid algorithms are made and tested for solving application problems that arise when modeling in the construction industry and modeling processes ductile fracture of thick-walled pipes defective items thinning of the mechanism of pore formation. Software research and solving SLE with sparse matrices block-diagonal form with frame in conditions approximated as regular data introduced to the family of intelligent workstations "Inparkom" joint development of the V.M. Glushkov Institute of Cybernetics and SSPE "Electronmash" and tested on a supercomputer SCIT V.M. Glushkov Institute of Cybernetics of NAS of Ukraine.