A Hybrid Method for the Numerical Solution ofDiscrete - Time
نویسنده
چکیده
A discrete-time algebraic Riccati equation (DARE) is a set of non-linear equations. One of the oldest, best studied, numerical methods for solving it, is Newton's method. Finding a stabilizing starting guess which is already close to the desired solution is crucial. We propose to compute an approximate solution of the DARE by the (butterry) SZ algorithm applied to the corresponding symplectic pencil where zero and innnity eigenvalues are removed using an iterative deeation strategy. This algorithm is a fast, reliable and structure-preserving algorithm for computing the stable deeating subspace of the symplectic matrix pencil associated with the DARE. From this, a stabilizing starting guess for Newton's method is easily obtained. The resulting method is very eecient and produces highly accurate results. Numerical examples demonstrate the behavior of the resulting hybrid method.
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