The SOR-k Method for Linear Systems with P-Cyclic Matrices
Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth power of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. In this paper, we first show that the optimal parameter of the SOR-k method as a function of k is strictly increasing. The behaviour of the spectral radius of the SOR-k method (for fixed parameter) is then studied.
Wang, L., Zhu, J., & Li, X. (2010). The SOR-k method for linear systems with p-cyclic matrices. International Journal of Computer Mathematics, 87(8), 1785-1794. doi:10.1080/00207160802464605