{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T10:25:12Z","timestamp":1757586312695},"reference-count":5,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":3721,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1995,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that a certain matrix norm ratio studied by Parlett has a supermum that is <jats:italic>O<\/jats:italic>(<jats:styled-content>\\documentclass{article}\\pagestyle{empty}\\begin{document}$\\mathop \\[\\sqrt n \\] $\\end{document}<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/tex2gif-ueqn-1.gif\" xlink:title=\"equation image\" \/><\/jats:styled-content>) when the chosen norm is the Frobenius norm, while it is <jats:italic>O<\/jats:italic>(log <jats:italic>n<\/jats:italic>) for the 2\u2010norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an <jats:italic>n<\/jats:italic> by <jats:italic>n<\/jats:italic> matrix.<\/jats:p>","DOI":"10.1002\/nla.1680020306","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:21:30Z","timestamp":1130872890000},"page":"243-250","source":"Crossref","is-referenced-by-count":6,"title":["On Parlett's matrix norm inequality for the Cholesky decomposition"],"prefix":"10.1002","volume":"2","author":[{"given":"Alan","family":"Edelman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Walter F.","family":"Mascarenhas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479893244717"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2039622"},{"key":"e_1_2_1_4_2","unstructured":"R.Mathias.Personal communication to B. Parlett 1991."},{"key":"e_1_2_1_5_2","unstructured":"B. N.Parlett.Perturbation theory for QR. Lecture given at the Fourth SIAM Conference on Applied Linear Algebra Minneapolis September1991. Document in preparation."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01931293"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.1680020306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.1680020306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T02:39:59Z","timestamp":1694399999000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.1680020306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,5]]}},"alternative-id":["10.1002\/nla.1680020306"],"URL":"https:\/\/doi.org\/10.1002\/nla.1680020306","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,5]]}}}