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• W2034347866 abstract "We derive a new representation of Lagrangian subspaces in the form ${rm Im} Pi^Tbig[begin{smallmatrix}I Xend{smallmatrix}big]$, where $Pi$ is a symplectic matrix which is the product of a permutation matrix and a real orthogonal diagonal matrix, and $X$ satisfies $leftvert X_{ij}rightvert leq begin{cases}1 & text{if $i=j$,} sqrt{2} & text{if $ineq j$.} end{cases}$ This representation allows us to limit element growth in the context of doubling algorithms for the computation of Lagrangian subspaces and the solution of Riccati equations. It is shown that a simple doubling algorithm using this representation can reach full machine accuracy on a wide range of problems, obtaining invariant subspaces of the same quality as those computed by the state-of-the-art algorithms based on orthogonal transformations. The same idea carries over to representations of arbitrary subspaces and can be used for other types of structured pencils." @default.
• W2034347866 created "2016-06-24" @default.
• W2034347866 creator A5016940729 @default.
• W2034347866 creator A5031634329 @default.
• W2034347866 date "2012-01-01" @default.
• W2034347866 modified "2023-10-18" @default.
• W2034347866 title "Doubling Algorithms with Permuted Lagrangian Graph Bases" @default.
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• W2034347866 doi "https://doi.org/10.1137/110850773" @default.
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