{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:34:38Z","timestamp":1760232878795,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,2]],"date-time":"2022-12-02T00:00:00Z","timestamp":1669939200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"],"award-info":[{"award-number":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"],"award-info":[{"award-number":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Higher Education Institutions of China","award":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"],"award-info":[{"award-number":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"],"award-info":[{"award-number":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Qing Lan Project of the Jiangsu Higher Education Institutions","award":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"],"award-info":[{"award-number":["12001396","12201302","BK20170591","BK20200268","21KJB110017","20KJB110005","2018M642130"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we propose a shift-deflation technique for the generalized eigenvalue problems. This technique consists of the following two stages: the shift of converged eigenvalues to zeros, and the deflation of these shifted eigenvalues. By performing the above technique, we construct a new generalized eigenvalue problem with a lower dimension which shares the same eigenvalues with the original generalized eigenvalue problem except for the converged ones. In addition, we consider the relations of the eigenvectors before and after performing the technique. Finally, numerical experiments show the effectiveness and robustness of the proposed method.<\/jats:p>","DOI":"10.3390\/sym14122547","type":"journal-article","created":{"date-parts":[[2022,12,2]],"date-time":"2022-12-02T02:18:06Z","timestamp":1669947486000},"page":"2547","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Shift-Deflation Technique for Computing a Large Quantity of Eigenpairs of the Generalized Eigenvalue Problems"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Wei","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoping","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taizhou University, Taizhou 225300, China"},{"name":"Department of Mathematics, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xueying","family":"Shi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taizhou University, Taizhou 225300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"An","family":"Luo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Taizhou University, Taizhou 225300, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,2]]},"reference":[{"key":"ref_1","unstructured":"Saad, Y. 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Appl."},{"key":"ref_11","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":"ref_12","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":"ref_13","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s10444-021-09855-w","article-title":"Newton\u2019s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils","volume":"47","author":"Li","year":"2021","journal-title":"Adv. Comput. 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