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We propose a new method, based on the Schur form of a matrix pair and Riemannian optimization over the manifold\n \n \n $$U(n) \\times U(n)$$<\/jats:tex-math>\n \n \n U<\/mml:mi>\n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n \u00d7<\/mml:mo>\n U<\/mml:mi>\n (<\/mml:mo>\n n<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , that is, the Cartesian product of the unitary group with itself. While the developed theory holds for any closed set\n \n \n $$\\Omega $$<\/jats:tex-math>\n \n \u03a9<\/mml:mi>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , we focus on two cases that are the most common in applications: Hurwitz stability and Schur stability. For these cases, we develop publicly available efficient implementations. Numerical experiments show that the resulting algorithm outperforms existing methods.\n <\/jats:p>","DOI":"10.1007\/s11075-025-02140-7","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T05:59:40Z","timestamp":1751608780000},"page":"569-592","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finding the nearest $$\\Omega $$-stable pencil with Riemannian optimization"],"prefix":"10.1007","volume":"102","author":[{"given":"Vanni","family":"Noferini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lauri","family":"Nyman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,4]]},"reference":[{"issue":"3","key":"2140_CR1","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/s10208-005-0179-9","volume":"7","author":"PA Absil","year":"2007","unstructured":"Absil, P.A., Baker, C., Gallivan, K.: Trust-region methods on Riemannian manifolds. 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