The use of the factorization of five diagonal matrices by tridiagonal Toeplitz matrices

The aim of this paper is the use of the factorization of five-diagonal matrices as the product of two Toeplitz tridiagonal matrices. Either bounds for the inverse or numerical methods for solving linear systems may be derived. Some results will be extended to block five-diagonal matrices. Applications to the numerical solution of ODE and PDE together with numerical tests will be given