A GENERALISATION OF SYSTEMATIC RELAXATION METHODS FOR CONSISTENTLY ORDERED MATRICES

A systematic relaxation method is analysed for consistently ordered matrices as defined by Broyden (1964). The method is a generalisation of successive over-relaxation (S.O.R.). A relation is derived between the eigenvalues of the iteration matrix of the method and the eigenvalues of the Jacobi iteration matrix. For p-cyclic matrices, the method corresponds to using a special type of diagonal matrix instead of a single relaxation factor. For certain choices of this diagonal matrix, the method has a better asymptotic rate of convergence than S.O.R. and requires less calculations and computer store. © 1969 Springer-Verlag.