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: min@math.ntnu.edu.tw (T.-M. Huang), wwlin@math.nthu.edu.tw (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 -