TY - JOUR
T1 - Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations
AU - Huang, Tsung Ming
AU - Lin, Wen Wei
N1 - Funding Information:
∗ Corresponding author. E-mail addresses: [email protected] (T.-M. Huang), [email protected] (W.-W. Lin). 1 This work is partially supported by the National Science Council and the National Center for Theoretical Sciences of Taiwan.
PY - 2009/3/1
Y1 - 2009/3/1
N2 - In this paper, we propose structured doubling algorithms for the computation of the weakly stabilizing Hermitian solutions of the continuous- and discrete-time algebraic Riccati equations, respectively. Assume that the partial multiplicities of purely imaginary and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil, respectively, are all even and the C/DARE and the dual C/DARE have weakly stabilizing Hermitian solutions with property (P). Under these assumptions, we prove that if these structured doubling algorithms do not break down, then they converge to the desired Hermitian solutions globally and linearly. Numerical experiments show that the structured doubling algorithms perform efficiently and reliably.
AB - In this paper, we propose structured doubling algorithms for the computation of the weakly stabilizing Hermitian solutions of the continuous- and discrete-time algebraic Riccati equations, respectively. Assume that the partial multiplicities of purely imaginary and unimodular eigenvalues (if any) of the associated Hamiltonian and symplectic pencil, respectively, are all even and the C/DARE and the dual C/DARE have weakly stabilizing Hermitian solutions with property (P). Under these assumptions, we prove that if these structured doubling algorithms do not break down, then they converge to the desired Hermitian solutions globally and linearly. Numerical experiments show that the structured doubling algorithms perform efficiently and reliably.
KW - Algebraic Riccati equation
KW - Global and linear convergence
KW - Hermitian solution
KW - Purely imaginary eigenvalue
KW - Structured doubling algorithm
KW - Unimodular eigenvalue
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U2 - 10.1016/j.laa.2007.08.043
DO - 10.1016/j.laa.2007.08.043
M3 - Article
AN - SCOPUS:58349112763
SN - 0024-3795
VL - 430
SP - 1452
EP - 1478
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - 5-6
ER -