On a relaxed SOR-method applied to nonsymmetric linear systems

Nonsymmetric linear systems are by far not as common as syemmtric ones but nevertheless systems with nonsymmetric matrices appear, e. g., in the numerical solution of the biharmonic equation, the computation of splines or the solution of some special integral equations. The SOR-method applied to linear systems X = BX + C with skew-symmetric matrix B is studied. Described is a region in the complex plane which contains the eigenvalues of the SOR-operator. Using this information a relaxed SOR-method is proposed; bounds for the spectral radius of the iteration operator are derived. The advantage is that the values of the corresponding iteration parameters can be directly calculated from the norm of the given matrix.