The SOR-k Method for Linear System with P-Cyclic Matrices
International Journal of Computer Mathematics
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, Liancheng, Jiehua Zhu, Xiezhang Li.
"The SOR-k Method for Linear System with P-Cyclic Matrices."
International Journal of Computer Mathematics, 87 (8): 1785-1794.