On nonlinear SOR-like methods. II: Convergence of the SOR-Newton method for mildly nonlinear equations
[For part I see the third author ibid. 14, No. 1, 87-97 (1997; Zbl 0881.65038).] The nonlinear Gauss-Seidel method is often performed in a way such that the auxiliary one-dimensional problems are only approximately solved. From the theory of iterative methods for linear equations it is natural to multiply the one-dimensional corrections with overrelaxation factors \(\omega>1\). Local convergence results are derived and applied to systems of equations which arise from the discretization of the semilinear elliptic equation \(\Delta u+ f(u)=0\).
scientific article; zbMATH DE number 1054331
scientific article