• Corpus ID: 245837696

# 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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