Two-Step Relaxation Newton Method for Nonsymmetric Algebraic Riccati Equations Arising from Transport Theory

Algorithm 1

The relaxation Newton method.

  for 𝑘=0,1,2,….

        with a given initial approximation 𝑥₀ of 𝑥_𝑘+1;

        for 𝑚=0,1,…,𝑀

      𝐹₂(𝑥_𝑘,𝑥_𝑚)Δ𝑥_𝑚=−𝐹(𝑥_𝑘,𝑥_𝑚),

      𝑥_𝑚+1=𝑥_𝑚+Δ𝑥_𝑚,

        end

        𝑥_𝑘+1=Δ𝑥_𝑀

  end