Global monotone convergence of Newton iteration for a nonlinear eigen-problem Original Research Article

The nonlinear eigen-problem image Ax+F(x)=λx,where A is an n×n irreducible Stieltjes matrix, is considered. Sufficient conditions are given, such that the problem has a unique positive solution and that the Newton iteration for solving this problem converges monotonically. The starting point of the iteration has to be a multiple of the positive eigenvector of A, but it does not need to be close to the solution x.