{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T12:12:03Z","timestamp":1773576723330,"version":"3.50.1"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2016,8,9]],"date-time":"2016-08-09T00:00:00Z","timestamp":1470700800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s11075-016-0185-9","type":"journal-article","created":{"date-parts":[[2016,8,9]],"date-time":"2016-08-09T01:02:38Z","timestamp":1470704558000},"page":"435-455","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Small sample statistical condition estimation for the total least squares problem"],"prefix":"10.1007","volume":"75","author":[{"given":"Huai-An","family":"Diao","sequence":"first","affiliation":[]},{"given":"Yimin","family":"Wei","sequence":"additional","affiliation":[]},{"given":"Pengpeng","family":"Xie","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,8,9]]},"reference":[{"key":"185_CR1","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1137\/090777608","volume":"32","author":"M Baboulin","year":"2011","unstructured":"Baboulin, M., Gratton, S.: A contribution to the conditioning of the total least squares problem. SIAM J. Matirx. Anal. Appl. 32, 685\u2013699 (2011)","journal-title":"SIAM J. Matirx. Anal. Appl."},{"key":"185_CR2","doi-asserted-by":"crossref","unstructured":"Baboulin, M., Gratton, S., Lacroix, R., Laub, A.: Efficient computation of condition estimates for linear least squares problems. In: Proceedings of the 10th International Conference on Parallel Processing and Applied Mathematics, PPAM 2013. Lecture Notes in Computer Science, vol. 8384, pp. 124\u2013133. Springer-Verlag (2014)","DOI":"10.1007\/978-3-642-55224-3_13"},{"key":"185_CR3","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1137\/040612233","volume":"27","author":"A Beck","year":"2005","unstructured":"Beck, A., Ben-Tal, A.: A global solution for the structured total least squares problem with block circulant matrices. SIAM J. Matrix Anal. Appl. 27, 238\u2013255 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR4","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1137\/050643696","volume":"29","author":"A Beck","year":"2007","unstructured":"Beck, A., Eldar, Y.C., Ben-Tal, A.: Mean-squared error estimation for linear systems with block circulant uncertainty. SIAM J. Matrix Anal. Appl. 29, 712\u2013730 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR5","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1137\/S0895479899355414","volume":"22","author":"\u00c5 Bj\u00f6rck","year":"2000","unstructured":"Bj\u00f6rck, \u00c5., Heggernes, P., Matstoms, P.: Methods for large scale total least squares problems. SIAM J. Matrix Anal. Appl. 22, 413\u2013429 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR6","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1090\/S0025-5718-06-01913-2","volume":"76","author":"F Cucker","year":"2007","unstructured":"Cucker, F., Diao, H., Wei, Y.: On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Math. Comp. 76, 947\u2013963 (2007)","journal-title":"Math. Comp."},{"issue":"5","key":"185_CR7","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1007\/s11425-013-4583-3","volume":"56","author":"H Diao","year":"2013","unstructured":"Diao, H., Shi, X., Wei, Y.: Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation. Sci. China Math. 56(5), 967\u2013982 (2013)","journal-title":"Sci. China Math."},{"key":"185_CR8","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.cam.2016.05.023","volume":"308","author":"H Diao","year":"2016","unstructured":"Diao, H., Wei, Y., Qiao, S.: Structured condition numbers of structured Tikhonov regularization problem and their estimations. J. Comp. Appl. Math. 308, 276\u2013300 (2016)","journal-title":"J. Comp. Appl. Math."},{"key":"185_CR9","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1002\/nla.790","volume":"19","author":"H Diao","year":"2012","unstructured":"Diao, H., Xiang, H., Wei, Y.: Mixed, componentwise condition numbers and small sample statistical condition estimation of Sylvester equations. Numer. Linear Algebra Appl. 19, 639\u2013654 (2012)","journal-title":"Numer. Linear Algebra Appl."},{"key":"185_CR10","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0024-3795(94)00209-6","volume":"234","author":"RD Fierro","year":"1996","unstructured":"Fierro, R.D., Bunch, J.R.: Perturbation theory for orthogonal projection methods with applications to least squares and total least squares. Linear Algebra Appl. 234, 71\u201396 (1996)","journal-title":"Linear Algebra Appl."},{"key":"185_CR11","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1137\/0614049","volume":"14","author":"I Gohberg","year":"1993","unstructured":"Gohberg, I., Koltracht, I.: Mixed, componentwise, and structured condition numbers. SIAM J. Matrix Anal. Appl. 14, 688\u2013704 (1993)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR12","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1137\/0717073","volume":"17","author":"GH Golub","year":"1980","unstructured":"Golub, G.H., Van Loan, C.F.: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883\u2013893 (1980)","journal-title":"SIAM J. Numer. Anal."},{"key":"185_CR13","doi-asserted-by":"crossref","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. Johns Hopkins University Press, Baltimore (2013)","edition":"4"},{"key":"185_CR14","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1137\/120895019","volume":"34","author":"S Gratton","year":"2013","unstructured":"Gratton, S., Titley-Peloquin, D., Ilunga, J.T.: Sensitivity and conditioning of the truncated total least squares solution. SIAM J. Matrix Anal. Appl. 34, 1257\u20131276 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"4","key":"185_CR15","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1137\/S0895479895296021","volume":"18","author":"T Gudmundsson","year":"1997","unstructured":"Gudmundsson, T., Kenney, C.S., Laub, A.J.: Small-sample statistical estimates for the sensitivity of eigenvalue problems. SIAM J. Matrix Anal. Appl 18 (4), 868\u2013886 (1997)","journal-title":"SIAM J. Matrix Anal. Appl"},{"key":"185_CR16","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1090\/psapm\/048\/1314843","volume":"48","author":"NJ Higham","year":"1994","unstructured":"Higham, N.J.: A survey of componentwise perturbation theory in numerical linear algebra. Proc. Symp. Appl. Math. 48, 49\u201377 (1994)","journal-title":"Proc. Symp. Appl. Math."},{"key":"185_CR17","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898718027","volume-title":"Accuracy and Stability of Numerical Algorithms","author":"NJ Higham","year":"2002","unstructured":"Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (2002)","edition":"2"},{"key":"185_CR18","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/s00211-013-0533-9","volume":"125","author":"Z Jia","year":"2013","unstructured":"Jia, Z., Li, B.: On the condition number of the total least squares problem. Numer. Math. 125, 61\u201387 (2013)","journal-title":"Numer. Math."},{"key":"185_CR19","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1007\/BF02510260","volume":"38","author":"J Kamm","year":"1998","unstructured":"Kamm, J., Nagy, J.: A total least squares method for Toeplitz systems of equations. BIT 38, 560\u2013582 (1998)","journal-title":"BIT"},{"key":"185_CR20","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1137\/0915003","volume":"15","author":"C Kenney","year":"1994","unstructured":"Kenney, C., Laub, A.: Small-sample statistical condition estimates for general matrix functions. SIAM J. Sci. Comput. 15, 36\u201361 (1994)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"185_CR21","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1137\/S1064827595282519","volume":"19","author":"C Kenney","year":"1998","unstructured":"Kenney, C., Laub, A., Reese, M.: Statistical condition estimation for linear systems. SIAM J. Sci. Comput. 19(2), 566\u2013583 (1998)","journal-title":"SIAM J. Sci. Comput."},{"key":"185_CR22","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1137\/S0895479895291935","volume":"19","author":"C Kenney","year":"1998","unstructured":"Kenney, C., Laub, A., Reese, M.: Statistical condition estimation for linear least squares. SIAM J. M.trix Anal. Appl. 19, 906\u2013923 (1998)","journal-title":"SIAM J. M.trix Anal. Appl."},{"key":"185_CR23","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1137\/070702242","volume":"31","author":"A Laub","year":"2008","unstructured":"Laub, A., Xia, J.: Statistical condition estimation for the roots of polynomials. SIAM J. Sci. Comput. 31, 624\u2013643 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"185_CR24","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1002\/nla.570","volume":"15","author":"A Laub","year":"2008","unstructured":"Laub, A., Xia, J.: Applications of statistical condition estimation to the solution of linear systems. Numer. Linear Algebra Appl. 15, 489\u2013513 (2008)","journal-title":"Numer. Linear Algebra Appl."},{"key":"185_CR25","doi-asserted-by":"crossref","first-page":"1658","DOI":"10.1137\/070707713","volume":"30","author":"A Laub","year":"2009","unstructured":"Laub, A., Xia, J.: Fast condition estimation for a class of structured eigenvalue problems. SIAM J. Matrix Anal. Appl. 30, 1658\u20131676 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR26","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1002\/nla.276","volume":"9","author":"P Lemmerling","year":"2002","unstructured":"Lemmerling, P., Van Huffel, S., De Moor, B.: The structured total least squares approach for nonlinearly structured matrices. Numer. Linear Algebra Appl. 9, 321\u2013332 (2002)","journal-title":"Numer. Linear Algebra Appl."},{"key":"185_CR27","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.laa.2010.07.022","volume":"435","author":"B Li","year":"2011","unstructured":"Li, B., Jia, Z.: Some results on condition numbers of the scaled total least squares problem. Linear Algebra Appl. 435, 674\u2013686 (2011)","journal-title":"Linear Algebra Appl."},{"key":"185_CR28","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1137\/S0895479898345813","volume":"22","author":"N Mastronardi","year":"2000","unstructured":"Mastronardi, N., Lemmerling, P., Van Huffel, S.: Fast structured total least squares algorithm for solving the basic deconvolution problem. SIAM J. Matrix Anal. Appl. 22, 533\u2013553 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR29","doi-asserted-by":"crossref","unstructured":"Mastronardi, N., Lemmerling, P., Van Huffel, S.: The structured total least squares problem. In: Olshevsky, V. (ed.) Structured Matrices in Mathematics, Computer Science and Engineering I : Part I of Contemporary Mathematics Book Series, vol. 280, pp 157\u2013175. American Mathematical Society, New York (2001)","DOI":"10.1090\/conm\/280\/04627"},{"key":"185_CR30","first-page":"217","volume":"3","author":"JR Rice","year":"1966","unstructured":"Rice, J.R.: A theory of condition. SIAM J. Numer. Anal. 3, 217\u2013232 (1966)","journal-title":"SIAM J. Numer. Anal."},{"key":"185_CR31","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1145\/322139.322148","volume":"26","author":"R Skeel","year":"1979","unstructured":"Skeel, R.: Scaling for numerical stability in Gaussian elimination. J. Assoc. Comput. Math. 26, 167\u2013169 (1979)","journal-title":"J. Assoc. Comput. Math."},{"key":"185_CR32","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971002","volume-title":"The Total Least Squares Problem: Computational Aspects and Analysis","author":"S Van Huffel","year":"1991","unstructured":"Van Huffel, S., Vandewalle, J.: The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, Philadelphia (1991)"},{"key":"185_CR33","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1137\/0613047","volume":"13","author":"M Wei","year":"1992","unstructured":"Wei, M.: The analysis for the total least squares problem with more than one solution. SIAM J. Matrix Anal. Appl. 13, 746\u2013763 (1992)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"185_CR34","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s11075-009-9269-0","volume":"51","author":"L Zhou","year":"2009","unstructured":"Zhou, L., Lin, L., Wei, Y., Qiao, S.: Perturbation analysis and condition numbers of scaled total least squares problems. Numer. Algorithms 51, 381\u2013399 (2009)","journal-title":"Numer. Algorithms"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-016-0185-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0185-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0185-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-016-0185-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,19]],"date-time":"2023-08-19T15:38:31Z","timestamp":1692459511000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-016-0185-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,8,9]]},"references-count":34,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["185"],"URL":"https:\/\/doi.org\/10.1007\/s11075-016-0185-9","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,8,9]]}}}