Chebyshev acceleration for SOR-like method

Abstract

There are several proposals for the generalization of Young’s successive over-relaxation (SOR) method to solve the saddle-point problem or augmented system. The most practical version is the SOR-like method (G.H. Golub et al., BIT, 41, 71–85, 2001), which was further studied by Li et al. (Int. J. Comput. Math., 81, 749–765, 2004) who found that the iteration matrix of the SOR-like method has no complex eigenvalues only under certain conditions. Motivated by the results of Li and co-authors, we consider the Chebyshev acceleration of the SOR-like method (GSOR-SI). First, the convergence of the GSOR-SI method is given. Secondly, it is shown that the asymptotic rate of the convergence of the GSOR-SI method is much larger than that of the SOR-like method, which indicates that the GSOR-SI method has a faster rate of convergence than the SOR-like method. Finally, numerical comparisons are given which show the GSOR-SI method is indeed faster than the SOR-like method.

Keywords:

• SOR method
• SOR-like method
• GSOR method
• Saddle-point problem
• Chebyshev acceleration