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An important special case is finding the nearest Hurwitz or Schur stable matrix, which has applications in systems theory. We describe a reformulation of the task as an optimization problem on the Riemannian manifold of orthogonal (or unitary) matrices. The problem can then be solved using standard methods from the theory of Riemannian optimization. The resulting algorithm is remarkably fast on small-scale and medium-scale matrices, and returns directly a Schur factorization of the minimizer, sidestepping the numerical difficulties associated with eigenvalues with high multiplicity.\n<\/jats:p>","DOI":"10.1007\/s00211-021-01217-4","type":"journal-article","created":{"date-parts":[[2021,8,3]],"date-time":"2021-08-03T03:42:33Z","timestamp":1627962153000},"page":"817-851","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Nearest $$\\varOmega $$-stable matrix via Riemannian optimization"],"prefix":"10.1007","volume":"148","author":[{"given":"Vanni","family":"Noferini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"Poloni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,3]]},"reference":[{"key":"1217_CR1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244","volume-title":"Optimization Algorithms on Matrix Manifolds","author":"P-A Absil","year":"2008","unstructured":"Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. 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