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A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations — arXiv:2608.22406

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.22406
License (as archived): CC0-1.0
Archived: 2026-10-18T08:27:35.854Z
SHA-256 of the archived text: 4ac36d466b648c490bbdb47ba4fc9ac4b6f89150685af853049efadca4a6c863
Stable URL of this page: https://metraipolis.com/documento/dc_7e84d47841fa

How to cite

A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations — arXiv:2608.22406 — arXiv (en), https://arxiv.org/abs/2608.22406 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7e84d47841fa (Metraipolis archive dc_7e84d47841fa, sha256 4ac36d466b648c490bbdb47ba4fc9ac4b6f89150685af853049efadca4a6c863)

BibTeX

@misc{dc7e84d47841fa,
  title = {A New Generalized Low-Rank Cholesky Factor ADI Algorithm for Large-Scale Stein Equations — arXiv:2608.22406},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.22406},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7e84d47841fa; sha256 4ac36d466b648c490bbdb47ba4fc9ac4b6f89150685af853049efadca4a6c863},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.22406. 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 solver for large-scale Stein equations with low-rank solutions. This paper shows that, as in the continuous-time Lyapunov equation case, the low-rank Cholesky factor ADI (LRCF-ADI) method for Stein equations implicitly performs $\mathcal{H}_2$-pseudo-optimal model order reduction for discrete-time systems. This observation leads to an automatic shift-generation strategy, allowing LRCF-ADI to select subsequent shifts without user intervention. The standard LRCF-ADI method requires shifts outside the unit circle. We generalize the method to allow shifts anywhere in the complex plane, including on the unit circle. This extension enables numerical integration for frequency-limited Stein equations by interpolating the integrand at points on the unit circle. It also enables non-intrusive, data-driven balanced truncation and frequency-limited balanced truncation using experimentally measurable transfer function samples on the unit circle, without requiring access to a state-space realization. Numerical results for large-scale models demonstrate the effectiveness of the proposed methods as low-rank Stein equation solvers and data-driven model order reduction methods.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA) ; Systems and Control (eess.SY).
Pagina del lavoro: https://arxiv.org/abs/2608.22406 — 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 2026-10-18T08:27:23.842Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).