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Newton’s method for solving cross-coupled sign-indefinite algebraic Riccati equations for weakly coupled large-scale systems. (English) Zbl 1118.65048
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.
65H10Systems of nonlinear equations (numerical methods)
15A24Matrix equations and identities
65L05Initial value problems for ODE (numerical methods)
91A23Differential games (game theory)
34A30Linear ODE and systems, general