Method of reducing the dimension of matrices of systems of linear equations and transformation to tridiagonal form in solving economic problems

A method of reducing the dimensionality of matrices is proposed for solving systems of linear equations in problems with high dimensionality. An algorithm is given for the method of reducing sparse matrices of systems of linear equations to a tridiagonal form in order to apply the sweep method to solve systems, which speeds up the calculation process. The application of these methods will allow more efficient use of computing system resources when solving high-dimensional problems in economics and other scientific fields.