On the solution of the rational matrix equation X = Q + LX-1LT
EURASIP Journal on Applied Signal Processing
Journal of Computational and Applied Mathematics
Brief paper: Perturbation analysis and condition numbers of symmetric algebraic Riccati equations
Automatica (Journal of IFAC)
Journal of Computational and Applied Mathematics
Positive definite solutions of the matrix equations X±A*X-q A=Q(q≥1)
Computers & Mathematics with Applications
The Matrix Equation $X+A^TX^{-1}A=Q$ and Its Application in Nano Research
SIAM Journal on Scientific Computing
On the numerical solution of large-scale sparse discrete-time Riccati equations
Advances in Computational Mathematics
Solving a Structured Quadratic Eigenvalue Problem by a Structure-Preserving Doubling Algorithm
SIAM Journal on Matrix Analysis and Applications
Alternating-directional Doubling Algorithm for $M$-Matrix Algebraic Riccati Equations
SIAM Journal on Matrix Analysis and Applications
On a Nonlinear Matrix Equation Arising in Nano Research
SIAM Journal on Matrix Analysis and Applications
Solving large-scale continuous-time algebraic Riccati equations by doubling
Journal of Computational and Applied Mathematics
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In this paper, we introduce the doubling transformation, a structure-preserving transformation for symplectic pencils, and present its basic properties. Based on these properties, a unified convergence theory for the structure-preserving doubling algorithms for a class of Riccati-type matrix equations is established, using only elementary matrix theory.