Solving of a system of linear algebraic equations with a three-diagonal matrix: a new look at the Cramer method

For the numerical solution of a system of linear algebraic equations with a three-diagonal matrix, a recursive version of the Cramer method is proposed. This method does not require additional restrictions on the system matrix, similar to those formulated for the sweep method. The results of numerical experiments are presented on a large set of test problems, a comparative analysis of the effectiveness of the proposed methodology and the corresponding algorithms is given.