Abstract:
In this article, on the basis of nonnegative matrices, some preconditioners from class of $(I+S)$-type based on the SOR method have been studied. Moreover, we prove the monotonicity of spectral radiuses of iterative matrices with respect to the parameters in [12]. Also, some splittings and preconditioners are compared and derived by comparisons. A numerical example is also given to illustrate our results.
Key words:preconditioning, comparison theorems, spectral radius, SOR, $L$-, $M$-matrix.