# Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem

@inproceedings{Guo2022GlobalMC, title={Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem}, author={Pei-Chang Guo}, year={2022} }

The nonlinear eigen-problem Ax+ F(x) = λx is studied where A is an n × n irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the positive eigenvector of A, the Newton-like iteration for this problem converges monotonically. Numerical results illustrate the effectiveness of this Newton-like method.

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