Spectral optimization of explicit iterative methods. I

Methods of constructing preconditioning of explicit iterative methods of solving systems of linear, algebraic equations with sparse matrices are considered in the work. The techniques considered can, first of all, be realized within the framework of the simplest data structures; secondly, the graph structures of the corresponding algorithms are well adapted to realization on parallel computers; thirdly, in conjunction with modifications of Chebyshev methods they make it possible to construct rather effective computational algorithms. Experimental data are presented which demonstrate the effect of the proposed techniques of preconditioning of the distribution of the eigenvalues of matrices of systems arising in discretization of two-dimensional elliptic boundary-value problems.