Newton’s method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems. (English) Zbl 1118.65048

Mukaidani, Hiroaki

Appl. Math. Comput. 188, No. 1, 103-115 (2007).

Summary: A new algorithm for solving cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) for weakly coupled large-scale systems is proposed. It is shown that since the proposed algorithm is based on the Newton’s method, the quadratic convergence is attained. Moreover, the local uniqueness of the convergence solutions for the CSAREs is investigated. Finally, in order to overcome the computation of large- and sparse-matrix related to the Newton’s method, the fixed point algorithm and the alternating direction implicit method are combined.

MSC:

65H10	Numerical computation of solutions to systems of equations
15A24	Matrix equations and identities
65L05	Numerical methods for initial value problems involving ordinary differential equations
91A23	Differential games (aspects of game theory)
34A30	Linear ordinary differential equations and systems

Keywords:

Newton-Kantorovich theorem; fixed point algorithm; alternating direction implicit method; linear-quadratic differential games; convergence; quadratic convergence

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