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Large-scale algebraic Riccati equations with high-rank constant terms. (English) Zbl 1418.65061

Summary: We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the previously successful methods based on low-rank representations are not directly applicable. We modify the doubling algorithm, making use of the low-rank in the input matrix \(B\). We also solve the challenging problems in the estimation of residuals and relative errors, convergence control and the output of the modified algorithm. Illustrative numerical examples are presented.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities

Software:

MESS; Matlab
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Full Text: DOI

References:

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