Solution of Large Sparse Nonlinear Systems by Monotone Convergent Iterations and Applications

In this paper we describe a family of Gauss‐Seidel‐iterations for the solution of large sparse nonlinear systems of equations Fx = 0. The mapping F is off‐diagonally antitone and strictly diagonally isotone. For suitable starting vectors every method of this family is monotonically convergent with respect to both sides. The iteration processes will be applied among others to the numerical solution of boundary value problems of quasilinear potential equations.