MAIN CONVERGENCE THEOREMS FOR THE IMPROVED SOR METHOD WITH ORDERINGS

To solve non-symmetric linear equations, we have already proposed a ge neralized SOR method, named the ''improved SOR method with orderings'' , and if we use special relaxation parameters and proper orderings, th en our method converges more rapidly and with fewer iterations than th e usual SOR method. In this paper, we consider main convergence theore ms for the improved SOR method with orderings and obtain useful conver gence theorems for the cases of tridiagonal matrices and also block tr idiagonal matrices which are ''decomposable to the tridiagonal matrice s''.