A direct method for solving circulant tridiagonal block systems of linear equations

This paper presents a modification of Rojo's algorithm [Comput. Math. Appl. 20 (1990) 61] to solve block circulant tridiagonal systems of linear equations which are Toeplitz and Hermitian. This new approach gives us a general direct algorithm for solving the problem. We will show how to choose a block matrix as a parameter to describe the method. We employ the factorization of block Toeplitz tridiagonal matrices as the product of two block Toeplitz subdiagonal and superdiagonal matrices. The algorithm is based on obtaining the solution of the nonlinear matrix equation A = Γ + B*Γ−1B. Finally, some numerical results will be given.