Solvers for systems of linear algebraic equations with block-band matrices

The article proposes methods for constructing fast solvers for systems of linear algebraic equations with block-band matrices. A data structure for efficient storage of such matrices in RAM and a fast algorithm for solving systems of linear equations with such matrices based on this structure are proposed. The article is focused on the creation of solvers based on iterative algorithms for solving systems of linear equations with both symmetric matrices and matrices having a saddle-point singularity. It is proposed to develop and use a special precompiler to speed up the solver. The experimental solver is implemented in C, and the preliminary compilation is based on the Optimizing Parallelizing System in this paper. The results of numerical experiments that demonstrate high efficiency of the developed methods, including the efficiency of the precompiler, are presented.