{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T17:11:19Z","timestamp":1781629879881,"version":"3.54.5"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004718","name":"Universit\u00e9 de Toulouse","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004718","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AAECC"],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We propose a way to unify the construction of Newton\u2019s methods for matrix decompositions. This construction is based on a perturbation analysis of a suitable system associated with matrix decompositions. Then it appears that the resolution of a linear Sylvester equation permits defining Newton\u2019s method. We give a general result to analyze the quadratic convergence of this Newton\u2019s method. We apply it to classical matrix decompositions:\n                    <jats:italic>LU<\/jats:italic>\n                    decomposition,\n                    <jats:italic>QR<\/jats:italic>\n                    decomposition, eigenproblem in the diagonalizable case, singular value decomposition, and Schur decomposition. Finally, we propose for future work a generalization of this construction to approximate matrix decomposition by high-order methods.\n                  <\/jats:p>","DOI":"10.1007\/s00200-025-00720-7","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T10:27:40Z","timestamp":1768386460000},"page":"541-570","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Unified Newton\u2019s method for matrix decompositions"],"prefix":"10.1007","volume":"37","author":[{"given":"Jean-Claude","family":"Yakoubsohn","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"720_CR1","unstructured":"Armentano, D., Yakoubsohn, J.-C.: High order numerical methods to approximate the singular value decomposition. hal-04197216. 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