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

Author

Listed:
  • Guo, Pei-Chang
  • Gao, Shi-Chen
  • Yang, Yong-Qing

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.

Suggested Citation

  • Guo, Pei-Chang & Gao, Shi-Chen & Yang, Yong-Qing, 2023. "Monotone convergence of Newton-like iteration for a structured nonlinear eigen-problem," Applied Mathematics and Computation, Elsevier, vol. 437(C).
    • Handle: RePEc:eee:apmaco:v:437:y:2023:i:c:s0096300322006063
    DOI: 10.1016/j.amc.2022.127532
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