{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T01:06:32Z","timestamp":1763082392052,"version":"3.45.0"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:00:00Z","timestamp":1744156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T00:00:00Z","timestamp":1744156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["JP17K18726","22H05107","JP19K03631","JP24K14843"],"award-info":[{"award-number":["JP17K18726","22H05107","JP19K03631","JP24K14843"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Optim Lett"],"published-print":{"date-parts":[[2025,12]]},"DOI":"10.1007\/s11590-025-02196-3","type":"journal-article","created":{"date-parts":[[2025,4,9]],"date-time":"2025-04-09T14:00:25Z","timestamp":1744207225000},"page":"1953-1977","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Expansions of the characteristic polynomial of a perturbed PSD matrix and convergence analysis of alternating projections for the PSD cone and a line"],"prefix":"10.1007","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9563-4852","authenticated-orcid":false,"given":"Yoshiyuki","family":"Sekiguchi","sequence":"first","affiliation":[]},{"given":"Hiroyuki","family":"Ochiai","sequence":"additional","affiliation":[]},{"given":"Hayato","family":"Waki","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,9]]},"reference":[{"issue":"2","key":"2196_CR1","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BF01027691","volume":"1","author":"HH Bauschke","year":"1993","unstructured":"Bauschke, H.H., Borwein, J.M.: On the convergence of von Neumann\u2019s alternating projection algorithm for two sets. Set-Val. Anal. 1(2), 185\u2013212 (1993)","journal-title":"Set-Val. Anal."},{"key":"2196_CR2","doi-asserted-by":"crossref","unstructured":"Borwein, J.M., Wolkowicz, H.: Facial reduction for a cone-convex programming problem. J. Aust. Math. Soc. 30(3), 369\u2013380 (1980\/81)","DOI":"10.1017\/S1446788700017250"},{"key":"2196_CR3","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/s10107-016-1048-9","volume":"162","author":"D Drusvyatskiy","year":"2017","unstructured":"Drusvyatskiy, D., Li, G., Wolkowicz, H.: A note on alternating projections for ill-posed semidefinite feasibility problems. Math. Program. 162, 537\u2013548 (2017)","journal-title":"Math. Program."},{"issue":"2","key":"2196_CR4","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1561\/2400000011","volume":"3","author":"D Drusvyatskiy","year":"2017","unstructured":"Drusvyatskiy, D., Wolkowicz, H.: The many faces of degeneracy in conic optimization. Found. Trends Optim. 3(2), 77\u2013170 (2017)","journal-title":"Found. Trends Optim."},{"key":"2196_CR5","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press (2017)"},{"key":"2196_CR6","volume-title":"Perturbation Theory for Linear Operator","author":"T Kato","year":"1980","unstructured":"Kato, T.: Perturbation Theory for Linear Operator. Springer-Verlag, Berlin (1980)"},{"key":"2196_CR7","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1137\/S0895479895294666","volume":"18","author":"J Moro","year":"1997","unstructured":"Moro, J., Burke, J.V., Overton, M.L.: On the Lidskii\u2013Vishik\u2013Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure. SIAM J. Matrix Anal. Appl. 18, 793\u2013817 (1997)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"2196_CR8","first-page":"143","volume-title":"First Order Eigenvalue Perturbation Theory and the Newton Diagram, Applied Mathematics and Scientific Computing (Dubrovnik, 2001)","author":"J Moro","year":"2003","unstructured":"Moro, J., Dopico, F.M.: First Order Eigenvalue Perturbation Theory and the Newton Diagram, Applied Mathematics and Scientific Computing (Dubrovnik, 2001), pp. 143\u2013175. Kluwer\/Plenum, New York (2003)"},{"key":"2196_CR9","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/s13160-023-00584-9","volume":"41","author":"H Ochiai","year":"2024","unstructured":"Ochiai, H., Sekiguchi, Y., Waki, H.: Exact convergence rates of alternating projections for nontransversal intersections. Jpn. J. Ind. Appl. Math. 41, 57\u201383 (2024)","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"2196_CR10","doi-asserted-by":"crossref","unstructured":"Ochiai, H., Sekiguchi, Y., Waki, H.: Analytic Formulas for Alternating Projection Sequences for the Positive Semidefinite Cone and an Application to Convergence Analysis, J. Math. Anal. Appl. 544 (1), Article 129070 (2025)","DOI":"10.1016\/j.jmaa.2024.129070"},{"key":"2196_CR11","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/s10957-020-01780-0","volume":"188","author":"Y Sekiguchi","year":"2021","unstructured":"Sekiguchi, Y., Waki, H.: Perturbation analysis of singular semidefinite programs and its applications to control problems. J. Optim. Theory Appl. 188, 52\u201372 (2021)","journal-title":"J. Optim. Theory Appl."}],"container-title":["Optimization Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-025-02196-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11590-025-02196-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11590-025-02196-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T01:02:43Z","timestamp":1763082163000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11590-025-02196-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,9]]},"references-count":11,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["2196"],"URL":"https:\/\/doi.org\/10.1007\/s11590-025-02196-3","relation":{},"ISSN":["1862-4472","1862-4480"],"issn-type":[{"type":"print","value":"1862-4472"},{"type":"electronic","value":"1862-4480"}],"subject":[],"published":{"date-parts":[[2025,4,9]]},"assertion":[{"value":"31 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 March 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}