{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:42:09Z","timestamp":1760265729185,"version":"build-2065373602"},"reference-count":20,"publisher":"Elsevier BV","issue":"9","license":[{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T00:00:00Z","timestamp":1682899200000},"content-version":"vor","delay-in-days":1461,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T00:00:00Z","timestamp":1556668800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The National Natural Science Foundation","doi-asserted-by":"publisher","award":["11671393"],"award-info":[{"award-number":["11671393"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers &amp; Mathematics with Applications"],"published-print":{"date-parts":[[2019,5]]},"DOI":"10.1016\/j.camwa.2018.12.025","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T13:48:57Z","timestamp":1547214537000},"page":"2396-2406","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":9,"title":["On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems"],"prefix":"10.1016","volume":"77","author":[{"given":"Zhong-Zhi","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cun-Qiang","family":"Miao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuai","family":"Jian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"year":"1998","series-title":"The Symmetric Eigenvalue Problem","author":"Parlett","key":"10.1016\/j.camwa.2018.12.025_b1"},{"key":"10.1016\/j.camwa.2018.12.025_b2","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1137\/0725078","article-title":"Criteria for combining inverse and Rayleigh quotient iteration","volume":"25","author":"Szyld","year":"1988","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.camwa.2018.12.025_b3","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/S0024-3795(98)10201-X","article-title":"The effects of inexact solvers in algorithms for symmetric eigenvalue problems","volume":"287","author":"Smit","year":"1999","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b4","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1137\/S0895479801399596","article-title":"Convergence analysis of inexact Rayleigh quotient iteration","volume":"24","author":"Notay","year":"2003","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b5","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.laa.2005.11.019","article-title":"Inexact inverse iteration for symmetric matrices","volume":"416","author":"Berns-M\u00fcller","year":"2006","journal-title":"Linear Algebra Appl."},{"year":"2011","series-title":"Numerical Methods for Large Eigenvalue Problems","author":"Saad","key":"10.1016\/j.camwa.2018.12.025_b6"},{"key":"10.1016\/j.camwa.2018.12.025_b7","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.laa.2017.01.018","article-title":"On local quadratic convergence of inexact simplified Jacobi-Davidson method","volume":"520","author":"Bai","year":"2017","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.aml.2017.03.021","article-title":"On local quadratic convergence of inexact simplified Jacobi-Davidson method for interior eigenpairs of Hermitian eigenproblems","volume":"72","author":"Bai","year":"2017","journal-title":"Appl. Math. Lett."},{"key":"10.1016\/j.camwa.2018.12.025_b9","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1137\/050623255","article-title":"Inexact inverse iteration with variable shift for nonsymmetric generalized eigenvalue problems","volume":"28","author":"Berns-M\u00fcller","year":"2006","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b10","first-page":"40","article-title":"Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem","volume":"28","author":"Freitag","year":"2007","journal-title":"Electron. Trans. Numer. Anal."},{"key":"10.1016\/j.camwa.2018.12.025_b11","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s10543-006-0100-1","article-title":"Convergence of inexact inverse iteration with application to preconditioned iterative solves","volume":"47","author":"Freitag","year":"2007","journal-title":"BIT"},{"key":"10.1016\/j.camwa.2018.12.025_b12","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1093\/imanum\/drm036","article-title":"A tuned preconditioner for inexact inverse iteration applied to Hermitian eigenvalue problems","volume":"28","author":"Freitag","year":"2008","journal-title":"IMA J. Numer. Anal."},{"key":"10.1016\/j.camwa.2018.12.025_b13","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1016\/j.laa.2007.11.013","article-title":"Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves","volume":"428","author":"Freitag","year":"2008","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b14","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1023\/A:1021930421106","article-title":"Inexact Rayleigh quotient-type methods for eigenvalue computations","volume":"42","author":"Simoncini","year":"2002","journal-title":"BIT"},{"key":"10.1016\/j.camwa.2018.12.025_b15","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1137\/080712908","article-title":"Convergence analysis of iterative solvers in inexact Rayleigh quotient iteration","volume":"31","author":"Xue","year":"2009","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/j.camwa.2018.12.025_b16","doi-asserted-by":"crossref","first-page":"21","DOI":"10.4208\/eajam.160816.131016a","article-title":"A filtered-Davidson method for large symmetric eigenvalue problems","volume":"7","author":"Miao","year":"2017","journal-title":"East Asian J. Appl. Math."},{"key":"10.1016\/j.camwa.2018.12.025_b17","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0377-0427(02)00822-1","article-title":"On the convergence of additive and multiplicative splitting iterations for systems of linear equations","volume":"154","author":"Bai","year":"2003","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.camwa.2018.12.025_b18","first-page":"179","article-title":"An algebraic convergence theorem for the multiplicative Schwarz iteration","volume":"12","author":"Bai","year":"2003","journal-title":"Numer. Math. J. Chin. Univ. (Engl. Ser.)"},{"year":"2013","series-title":"Matrix Computations","author":"Golub","key":"10.1016\/j.camwa.2018.12.025_b19"},{"key":"10.1016\/j.camwa.2018.12.025_b20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00211-004-0521-1","article-title":"Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems","volume":"98","author":"Bai","year":"2004","journal-title":"Numer. Math."}],"container-title":["Computers &amp; Mathematics with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122118307235?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0898122118307235?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T10:06:44Z","timestamp":1760263604000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0898122118307235"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5]]},"references-count":20,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["S0898122118307235"],"URL":"https:\/\/doi.org\/10.1016\/j.camwa.2018.12.025","relation":{},"ISSN":["0898-1221"],"issn-type":[{"type":"print","value":"0898-1221"}],"subject":[],"published":{"date-parts":[[2019,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On multistep Rayleigh quotient iterations for Hermitian eigenvalue problems","name":"articletitle","label":"Article Title"},{"value":"Computers & Mathematics with Applications","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.camwa.2018.12.025","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2018 Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}