Large-scale discrete-time algebraic Riccati equations— Doubling algorithm and error analysis
نویسندگان
چکیده
منابع مشابه
Solving Large-Scale Discrete-Time Algebraic Riccati Equations by Doubling
We consider the solution of large-scale discrete-time algebraic Riccati equations with numerically low-ranked solutions. The structure-preserving doubling algorithm will be adapted, with the iterates for A not explicitly computed but in the recursive form Ak = A 2 k−1 − D (1) k S −1 k [D (2) k ] >, where D (1) k and D (2) k are low-ranked with S −1 k being small in dimension. With n being the d...
متن کاملSolving large-scale continuous-time algebraic Riccati equations by doubling
We consider the solution of large-scale algebraic Riccati equations with numerically lowranked solutions. For the discrete-time case, the structure-preserving doubling algorithm has been adapted, with the iterates for A not explicitly computed but in the recursive form Ak = A 2 k−1 −D (1) k S −1 k [D (2) k ] >, with D (1) k and D (2) k being low-ranked and S −1 k being small in dimension. For t...
متن کاملLarge-Scale Discrete-Time Algebraic Riccati Equations — Numerically Low-Ranked Solution, SDA and Error Analysis∗
We consider the solution of large-scale discrete-time algebraic Riccati equations with numerically low-ranked solutions. The structure-preserving doubling algorithm (SDA) will be adapted, with the iterates for A not explicitly computed but in the recursive form Ak = Ak−1−D (1) k Sk[D (2) k ] >, where D (1) k and D (2) k are low-ranked with Sk being small in dimension. With n being the dimension...
متن کاملSolving Large-Scale Nonsymmetric Algebraic Riccati Equations by Doubling
We consider the solution of the large-scale nonsymmetric algebraic Riccati equation XCX − XD − AX + B = 0, with M ≡ [D,−C;−B,A] ∈ R(n1+n2)×(n1+n2) being a nonsingular M-matrix, and A,D being sparse-like (with the products A−1v, A−>v, D−1v and D−>v computable in O(n1) or O(n2) complexity, for some vector v) and B,C are low-ranked. The structure-preserving doubling algorithm by Guo, Lin and Xu (2...
متن کاملA Structured Doubling Algorithm for Discrete-time Algebraic Riccati Equations with Singular Control Weighting Matrices
In this paper we propose a structured doubling algorithm for solving discrete-time algebraic Riccati equations without the invertibility of control weighting matrices. In addition, we prove that the convergence of the SDA algorithm is linear with ratio less than 1 2 when all unimodular eigenvalues of the closed-loop matrix are semisimple. Numerical examples are shown to illustrate the feasibili...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2015
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.09.005