This paper is concerned with the convergence of a two-step modified Newton method for solving the nonlinear system arising from the minimal nonnegative solution of nonsymmetric algebraic Riccati equations from neutron transport theory. We show the monotonic convergence of the two-step modified Newton method under mild assumptions. When the Jacobian of the nonlinear operator at the minimal positive solution is singular, we present a convergence analysis of the two-step modified Newton method in this context. Numerical experiments are conducted to demonstrate that the proposed method yields comparable results to several existing Newton-type methods and that it brings a significant reduction in computation time for nearly singular and large-scale problems.

翻译：本文研究用于求解中子输运理论中非对称代数Riccati方程最小非负解所产生非线性系统的两步修正牛顿法的收敛性。我们在温和假设条件下证明了两步修正牛顿法的单调收敛性。当非线性算子在最小正解处的雅可比矩阵奇异时，我们在此背景下给出了两步修正牛顿法的收敛性分析。数值实验表明，所提方法可获得与现有多种牛顿型方法相当的计算结果，且对于近奇异和大规模问题能显著减少计算时间。