Reduction of unknowns in solving systems of linear algebraic equations by means of Yanenko's sweep

The article deals with the question of the application of Yanenko's parametric parallel sweep for the reduction of unknowns in the solution of linear algebraic equations arising in finite-difference approximation of problems for differential equations. Two-diagonal and tridiagonal matrices are considered. In the case of a subinterval of a partition with a small number of nodes (1-2-3), the pre-solving phase of auxiliary tasks can be performed analytically, without recourse to computing on the computer. The proposed approach is compared with the method of cyclic reduction and its wider possibilities are demonstrated. It seems that the proposed approach can be used to increase the degree of parallelism in the parallel (simultaneous) solution of the problems under consideration on multiprocessor computing devices.