Naslov
RADI : a low-rank ADI-type algorithm for large scale algebraic Riccati equations

Autori
Benner, Peter ; Bujanović, Zvonimir ; Kürschner, Patrick ; Saak, Jens

Izvornik
Numerische Mathematik (0029-599X) 138 (2018), 2; 301-330

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
matrix equations ; algebraic Riccati equations ; ADI iteration ; low rank approximation ; Hamiltonian matrix ; subspace iteration

Sažetak
In recent years, several new approaches for solving the large-scale continuous-time algebraic Riccati equation have appeared in the literature. Amodei and Buchot suggest computing a low-dimensional invariant subspace of the associated Hamiltonian matrix. Simoncini and Lin also target the Hamiltonian matrix, but in a different way: they iterate on the Cayley-transformed matrix with various shifts. Wong and Balakrishnan directly generalize the Lyapunov ADI-method to the Riccati equation. In this paper we introduce another method, inspired by the Cholesky-factored variant of the Lyapunov ADI-method. The advantage of the new algorithm is in its immediate and efficient low-rank formulation, and a simpler implementation compared to the three algorithms mentioned above. We discuss the theoretical properties of the new method, as well as various shift selection strategies. Finally, we show that all of the seemingly different methods listed above in fact produce exactly the same iterates when used with the same parameters: they are algorithmically different descriptions of the same approximation sequence to the Riccati solution.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA