Monotone convergence of Newton-like iteration for a structured nonlinear eigen-problem

Pei-Chang Guo, Shi-Chen Gao and Yong-Qing Yang

Applied Mathematics and Computation, 2023, vol. 437, issue C

Abstract: A structured eigen-problem Ax+F(x)=λx is studied in this paper, where in applications A∈Rn×n is an irreducible Stieltjes matrix. Under certain restrictions, this problem has a unique positive solution. We show that, starting from a multiple of the positive eigenvector of A, the Newton-like algorithm for this eigen-problem is well defined and converges monotonically. Numerical results illustrate the effectiveness of this Newton-like method.

Keywords: Eigen-problem; Stieltjes matrix; Newton-like method; Monotone convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322006063

DOI: 10.1016/j.amc.2022.127532

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