{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:49:56Z","timestamp":1773233396948,"version":"3.50.1"},"reference-count":7,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":3782,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1995,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The QR algorithm is a basic algorithm for computing the eigenvalues of dense matrices. For efficiency reasons it is prerequisite that the algorithm is applied only after the original matrix has been reduced to a matrix of a particular shape, most notably Hessenberg and tridiagonal, which is preserved during the iterative process. In certain circumstances a reduction to another matrix shape may be advantageous. In this paper, we identify which zero patterns of symmetric matrices are preserved under the QR algorithm.<\/jats:p>","DOI":"10.1002\/nla.1680020203","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T17:52:09Z","timestamp":1130867529000},"page":"87-93","source":"Crossref","is-referenced-by-count":12,"title":["Matrix shapes invariant under the symmetric QR algorithm"],"prefix":"10.1002","volume":"2","author":[{"given":"Peter","family":"Arbenz","sequence":"first","affiliation":[]},{"given":"Gene H.","family":"Golub","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"The Symmetric Eigenvalue Problem","author":"Parlett B. N.","year":"1980"},{"key":"e_1_2_1_3_2","volume-title":"Fundamentals of Matrix Computations","author":"Watkins D. S.","year":"1991"},{"key":"e_1_2_1_4_2","volume-title":"LAPACK Users' Guide","author":"Anderson E.","year":"1992"},{"key":"e_1_2_1_5_2","first-page":"655","article-title":"SIAM J. Matrix","volume":"13","author":"Arbenz P.","year":"1992","journal-title":"Anal. Appl."},{"key":"e_1_2_1_6_2","volume-title":"Data Structures and Algorithms","author":"Aho A. V.","year":"1983"},{"key":"e_1_2_1_7_2","volume-title":"Computer Solution of Large Sparse Positive Definite Systems","author":"George A.","year":"1981"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90213-8"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.1680020203","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.1680020203","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T02:36:14Z","timestamp":1694399774000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.1680020203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,3]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,3]]}},"alternative-id":["10.1002\/nla.1680020203"],"URL":"https:\/\/doi.org\/10.1002\/nla.1680020203","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,3]]}}}