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Iterative and doubling algorithms for Riccati-type matrix equations: a comparative introduction
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 of another naturally-arising fixed-point
iteration via a sort of repeated squaring.
The equations we consider are Stein equations , Lyapunov
equations , discrete-time algebraic Riccati equations
, continuous-time algebraic Riccati equations
, palindromic quadratic matrix equations , and
nonlinear matrix equations . 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.Comment: Review article for GAMM Mitteilunge
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