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Numer. Anal."],"published-print":{"date-parts":[[2025,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The parallel orbital-updating approach is an orbital\/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure calculations. In this paper, based on the investigation of a quasi-orthogonality, we present the numerical analysis of the parallel orbital-updating approach for linear eigenvalue problems, including convergence and error estimates of the numerical approximations.<\/jats:p>","DOI":"10.1137\/24m1690084","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T14:29:18Z","timestamp":1755872958000},"page":"1886-1908","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Analysis of the Parallel Orbital-Updating Approach for Eigenvalue Problems"],"prefix":"10.1137","volume":"63","author":[{"given":"Xiaoying","family":"Dai","sequence":"first","affiliation":[{"name":"SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-3738-6540","authenticated-orcid":true,"given":"Yan","family":"Li","sequence":"additional","affiliation":[{"name":"SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-4571-8422","authenticated-orcid":true,"given":"Bin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 102206 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aihui","family":"Zhou","sequence":"additional","affiliation":[{"name":"SKLMS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"ref1","unstructured":"Quantum ESPRESSO, http:\/\/www.quantum-espresso.org\/, 2024."},{"key":"ref2","volume-title":"Sobolev Spaces","author":"Adams R. 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