Metraipolis › archive › dc_e18528690da1

D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations — arXiv:2608.29131

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.29131
License (as archived): CC0-1.0
Archived: 2026-10-17T09:28:24.793Z
SHA-256 of the archived text: 167a50c9d62f58cfc24c1c082fa89d3f8df0a0de146026439856c10a4512233d
Stable URL of this page: https://metraipolis.com/documento/dc_e18528690da1

How to cite

D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations — arXiv:2608.29131 — arXiv (en), https://arxiv.org/abs/2608.29131 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e18528690da1 (Metraipolis archive dc_e18528690da1, sha256 167a50c9d62f58cfc24c1c082fa89d3f8df0a0de146026439856c10a4512233d)

BibTeX

@misc{dce18528690da1,
  title = {D-RADI: A Low-rank ADI Algorithm for Solving Large-scale Discrete-time Algebraic Riccati Equations — arXiv:2608.29131},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.29131},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e18528690da1; sha256 167a50c9d62f58cfc24c1c082fa89d3f8df0a0de146026439856c10a4512233d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.29131. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The low-rank alternating direction implicit (ADI) method is an efficient numerical technique for solving several types of large-scale matrix equations that admit low-rank solutions. The discrete-time algebraic Riccati equation (DARE) is an important matrix equation with applications in state estimation, controller design, and filter design. In the literature, the low-rank Cholesky factor ADI method for Stein equations has been used within Newton iterations to solve large-scale DAREs. However, no dedicated low-rank ADI solver is available for such DAREs. To address this gap, this paper presents a low-rank ADI solver for large-scale DAREs. We also propose an efficient approach to generate ADI shifts automatically, which makes the proposed solver fully autonomous for solving DAREs. The effectiveness of the proposed solver is compared with MATLAB's \texttt{idare} on a moderate-order problem. Efficiency and accuracy are further demonstrated on large-scale DAREs of order $10^6$. Numerical results confirm that the solver is efficient, accurate, and fully autonomous.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-01 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2608.29131 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T08:59:54.347Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).