{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T11:04:14Z","timestamp":1779879854429,"version":"3.53.1"},"reference-count":48,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["123B1008"],"award-info":[{"award-number":["123B1008"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271108"],"award-info":[{"award-number":["12271108"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U24A2001"],"award-info":[{"award-number":["U24A2001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003399","name":"Science and Technology Commission of Shanghai Municipality","doi-asserted-by":"publisher","award":["23JC1400501"],"award-info":[{"award-number":["23JC1400501"]}],"id":[{"id":"10.13039\/501100003399","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2026,6,30]]},"DOI":"10.1137\/25m1788312","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T10:22:47Z","timestamp":1779877367000},"page":"649-672","source":"Crossref","is-referenced-by-count":0,"title":["Efficient Estimate for the Optimal Backward Error of the Multidimensional Total Least Squares"],"prefix":"10.1137","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-6514-9349","authenticated-orcid":true,"given":"Jiali","family":"Shan","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-0546","authenticated-orcid":true,"given":"Yimin","family":"Wei","sequence":"additional","affiliation":[{"name":"Corresponding author.\u00a0School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai 200433, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01231769"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/040616851"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479898333636"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899355414"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/060675691"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/nla.640"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"S. Chenakkod, M. Derezi\u0144ski, X. Dong, and M. Rudelson, Optimal embedding dimension for sparse subspace embeddings, in Proceedings of the 56th Annual ACM Symposium on Theory of Computing, 2024, pp. 1106\u20131117.","DOI":"10.1145\/3618260.3649762"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"M. B. Cohen, Nearly tight oblivious subspace embeddings by trace inequalities, in Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2016, pp. 278\u2013287, https:\/\/doi.org\/10.1137\/1.9781611974331.ch21.","DOI":"10.1137\/1.9781611974331.ch21"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022385611904"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-023-10061-z"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/23M1616790"},{"key":"ref12","first-page":"79","author":"Epperly E. N.","year":"2026","journal-title":"Comm. Pure Appl. Math."},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1137\/0717073"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/110825467"},{"key":"ref16","unstructured":"J. F. Grcar, Optimal Sensitivity Analysis of Linear Least Squares, Technical Report LBNL-52434, Lawrence Berkeley National Laboratory, Berkeley, CA, 2003."},{"key":"ref17","volume-title":"Estimates of Optimal Backward Perturbations for Linear Least Squares Problems","author":"Grcar J. F.","year":"2008"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895296446"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/090771806"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2020.07.020"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718027"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2006.877352"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/15M1028339"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1137\/100813348"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/120884237"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2018.06.016"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/21M1462155"},{"key":"ref28","volume-title":"Topics in Matrix Analysis","author":"Horn R. A.","year":"1994"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/BF02510356"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/21M1400420"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.856643"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492920000021"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s002110100314"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/070697835"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/25M1749657"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/16.1.1"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/BF02510179"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1137\/18M1201068"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396047"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971002"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1006\/jmra.1994.1209"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680020308"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396223"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1142\/10950"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2007.12.002"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1137\/24M1715209"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1137\/15M1053815"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T10:22:50Z","timestamp":1779877370000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1788312"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,6,30]]}},"alternative-id":["10.1137\/25M1788312"],"URL":"https:\/\/doi.org\/10.1137\/25m1788312","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]}}}