On the spectrum of the SOR operator for symmetric positive definite matrices (Q811083)

The successive overrelaxation (SOR) method for solving systems of linear algebraic equations with a positive definite coefficient matrix \(A=I-L- L^ T\) in which L is not necessarily strictly lower triangular is discussed. Especially, the authors study the behaviour of the spectrum of the SOR operator \(L_{\omega}\) for \(\omega\to 0\) and \(\omega\to 2\) and describe enclosure sets which can be used to estimate the spectral radius of \(L_{\omega}\) for \(0<\omega <2\).