Application of the generalized backward substitution method to solve a class of linear systems

A general purpose subprogram is given to solve linear systems corresponding to tridiagonal matrices in which the elements are replaced by submatrices. As an example, one can mention the discretized form (in time and space) of very general parabolic equations. A stable numerical scheme leads to such a system of linear equations. To solve these equations, they are generalized to matrices of the backward substitution method. (Auth.)