Convergence Analysis of Structure-Preserving Doubling Algorithms for Riccati-Type Matrix Equations
Wen‐Wei Lin, Shufang Xu · SIAM Journal on Matrix Analysis and Applications · 2006
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.