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On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces (CROSBI ID 224342)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Benner, Peter ; Bujanović, Zvonimir On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces // Linear algebra and its applications, 488 (2016), 430-459. doi: 10.1016/j.laa.2015.09.027

Podaci o odgovornosti

Benner, Peter ; Bujanović, Zvonimir

engleski

On the solution of large-scale algebraic Riccati equations by using low-dimensional invariant subspaces

This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a low-dimensional stable invariant subspace of the associated Hamiltonian matrix. We give conditions on AREs to admit solutions of low numerical rank and show that these can be approximated via Hamiltonian eigenspaces. We discuss strategies on choosing the proper eigenspace that yields a good approximation, and different formulas for building the approximation itself. Similarities of our approach with several other methods for solving AREs are shown: closely related are the projection-type methods that use various Krylov subspaces and the qADI algorithm. The aim of this paper is merely to analyze the possibilities of computing approximate Riccati solutions from low-dimensional subspaces related to the corresponding Hamiltonian matrix and to explain commonalities among existing methods rather than providing a new algorithm.

matrix equations ; algebraic Riccati equations ; Hamiltonian matrices ; invariant subspaces ; Krylov subspaces ; ADI iteration

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Podaci o izdanju

488

2016.

430-459

objavljeno

0024-3795

10.1016/j.laa.2015.09.027

Povezanost rada

Matematika

Poveznice
Indeksiranost