Improved SOR method with orderings and direct methods (Q1301573)

A generalized successive overrelaxation (SOR) method with multiple relaxation parameters is considered for solving a system of linear equations. Optimal choices of the parameters are examined under the assumption that the coefficient matrix is tridiagonal and regular. It is shown that the spectral radius of the iterative matrix is reduced to zero for a pair of parameter values which is computed from the pivots of the Gaussian elimination applied to the system. A proper choice of ordering and starting vectors for the iteration is also proposed. Furthermore, the application of the presented technique to a class of systems which includes Hessenberg systems is also discussed.