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- W4287777253 abstract "We review a family of algorithms for Lyapunov- and Riccati-type equations which are all related to each other by the idea of emph{doubling}: they construct the iterate $Q_k = X_{2^k}$ of another naturally-arising fixed-point iteration $(X_h)$ via a sort of repeated squaring. The equations we consider are Stein equations $X - A^*XA=Q$, Lyapunov equations $A^*X+XA+Q=0$, discrete-time algebraic Riccati equations $X=Q+A^*X(I+GX)^{-1}A$, continuous-time algebraic Riccati equations $Q+A^*X+XA-XGX=0$, palindromic quadratic matrix equations $A+QY+A^*Y^2=0$, and nonlinear matrix equations $X+A^*X^{-1}A=Q$. We draw comparisons among these algorithms, highlight the connections between them and to other algorithms such as subspace iteration, and discuss open issues in their theory." @default.
- W4287777253 created "2022-07-26" @default.
- W4287777253 creator A5031634329 @default.
- W4287777253 date "2020-05-18" @default.
- W4287777253 modified "2023-09-24" @default.
- W4287777253 title "Iterative and doubling algorithms for Riccati-type matrix equations: a comparative introduction" @default.
- W4287777253 doi "https://doi.org/10.48550/arxiv.2005.08903" @default.
- W4287777253 hasPublicationYear "2020" @default.
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