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.

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