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Zbl 1118.65048
Mukaidani, Hiroaki
Newton's method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems. (English)
[J] Appl. Math. Comput. 188, No. 1, 103-115 (2007). ISSN 0096-3003

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 2000:: *65H10 Systems of nonlinear equations (numerical methods)
15A24 Matrix equations
65L05 Initial value problems for ODE (numerical methods)
91A23 Differential games
34A30 Linear ODE and systems

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

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Zentralblatt MATH Berlin [Germany]