On one-parameter family of Newton-like iterations for solving nonsymmetric algebraic Riccati equation from transport theory.

*(English)*Zbl 1446.65026Summary: For the nonsymmetric algebraic Riccati equation arising from transport theory, it is known that this matrix equation can be translated to vector equations.

In the present paper, we concern with one-parameter family Newton-like iterations, which includes the method considered by Y. Lin et al. [IMA J. Numer. Anal. 28, No. 2, 215–224 (2008; Zbl 1144.65030)] as a special case, with cubic convergence to solve the minimal positive solution of the vector equations. We prove that the sequence of vectors generated by this family of Newton-like iterations starting from the zero vector is monotonically increasing and converges to the minimal positive solution of the vector equations.

Numerical experiments show the computational performance for this family of Newton-like iterations with various values of the parameter.

In the present paper, we concern with one-parameter family Newton-like iterations, which includes the method considered by Y. Lin et al. [IMA J. Numer. Anal. 28, No. 2, 215–224 (2008; Zbl 1144.65030)] as a special case, with cubic convergence to solve the minimal positive solution of the vector equations. We prove that the sequence of vectors generated by this family of Newton-like iterations starting from the zero vector is monotonically increasing and converges to the minimal positive solution of the vector equations.

Numerical experiments show the computational performance for this family of Newton-like iterations with various values of the parameter.

##### MSC:

65H10 | Numerical computation of solutions to systems of equations |

65F45 | Numerical methods for matrix equations |

15A24 | Matrix equations and identities |