In this paper we are concerned with the solution of the nonlinear system $Fx = 0$ by the nonlinear block Gauss–Seidel (NBGS) and the nonlinear block successive overrelaxation (NBSOR) methods. If F is an M-function, we give a theorem which compares the convergence rates of the NBGS method for different block groupings. For the NBSOR method, we describe an a posteriori numerical strategy for determining an optimum relaxation parameter ω which is based on an asymptotic application of the theory developed by Young for 2-cyclic matrices. We also give an inner iteration procedure based on Newton’s method for solving the block subsystems. Numerical results are included.
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Hageman et al. (1975) studied this question.
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