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Iterative rational Krylov algorithm — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T14:26:04.217Z
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Iterative rational Krylov algorithm — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_bd37519dfad1 (Metraipolis archive dc_bd37519dfad1, sha256 558ac717f2d9f982bffc8742ac7b23c66c0875e5150e828abe66f681cacc67ed)

BibTeX

@misc{dcbd37519dfad1,
  title = {Iterative rational Krylov algorithm — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_bd37519dfad1; sha256 558ac717f2d9f982bffc8742ac7b23c66c0875e5150e828abe66f681cacc67ed},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The iterative rational Krylov algorithm (IRKA) is an iterative algorithm, useful for model order reduction (MOR) of single-input single-output (SISO) linear time-invariant dynamical systems. At each iteration, IRKA does an Hermite type interpolation of the original system transfer function. Each interpolation requires solving r {\displaystyle r} shifted pairs of linear systems, each of size n × n {\displaystyle n\times n} ; where n {\displaystyle n} is the original system order, and r {\displaystyle r} is the desired reduced model order (usually r ≪ n {\displaystyle r\ll n} ). The algorithm was first introduced by Gugercin, Antoulas and Beattie in 2008. It is based on a first order necessary optimality condition, initially investigated by Meier and Luenberger in 1967. The first convergence proof of IRKA was given by Flagg, Beattie and Gugercin in 2012, for a particular kind of systems.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Numerical analysis»).
Fonte: Wikipedia in inglese, voce «Iterative rational Krylov algorithm» — https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm
Wikidata Q107292978 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q107292978
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Iterative_rational_Krylov_algorithm?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1369331641, consultata il 2026-10-07T14:07:16.038Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: d69b5006ae63a91c6b2800ec6e63afe426e43820ccb042a4c1224c6893a1e672