{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T17:44:32Z","timestamp":1774374272528,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T00:00:00Z","timestamp":1631232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s10444-021-09898-z","type":"journal-article","created":{"date-parts":[[2021,9,10]],"date-time":"2021-09-10T09:02:31Z","timestamp":1631264551000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Accurate singular values of a class of parameterized negative matrices"],"prefix":"10.1007","volume":"47","author":[{"given":"Rong","family":"Huang","sequence":"first","affiliation":[]},{"given":"Jungong","family":"Xue","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,10]]},"reference":[{"key":"9898_CR1","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s002110100289","volume":"90","author":"CAS Alfa","year":"2002","unstructured":"Alfa, C. A. S., Xue, J., Ye, Q.: Entrywise perturbation theory for diagonally dominant M-matrices with applications. Numer. Math. 90, 401\u2013141 (2002)","journal-title":"Numer. Math."},{"key":"9898_CR2","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1090\/S0025-5718-01-01325-4","volume":"71","author":"CAS Alfa","year":"2002","unstructured":"Alfa, C. A. S., Xue, J., Ye, Q.: Accurate computation of the smallest eigenvalue of a diagonally dominant M-matrix. Math. Comp. 71, 217\u2013236 (2002)","journal-title":"Math. Comp."},{"key":"9898_CR3","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/0024-3795(87)90313-2","volume":"90","author":"Y Ando","year":"1987","unstructured":"Ando, Y.: Totally positive matrices. Linear Algebra Appl. 90, 165\u2013219 (1987)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR4","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1137\/100794481","volume":"32","author":"CR Bevilacqua","year":"2011","unstructured":"Bevilacqua, C.R., Bozzo, E., Corso, G. M. D.: Qd-type methods for quasiseparable matrices. SIAM J. Matrix Anal. Appl. 32, 722\u2013747 (2011)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR5","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1137\/12088642X","volume":"34","author":"N Castro-Gonz\u00e1lez","year":"2013","unstructured":"Castro-Gonz\u00e1lez, N., Geballos, J., Dopico, F.M., Molera, J.M.: Accurate solution of structured least squares problems via rank-revealing decompositions. SIAM J. Matrix Anal. Appl. 34, 1112\u20131128 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR6","doi-asserted-by":"publisher","first-page":"1303","DOI":"10.1137\/130943613","volume":"35","author":"CM Dailey","year":"2014","unstructured":"Dailey, C. M., Dopico, F. M., Ye, Q.: Relative perturbation theory for diagonally dominant matrices. SIAM J. Matrix Anal. Appl. 35, 1303\u20131328 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR7","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1137\/13093858X","volume":"35","author":"CM Dailey","year":"2014","unstructured":"Dailey, C. M., Dopico, F. M., Ye, Q.: A new perturbation bound for the LDU factorization of diagonally dominant matrices. SIAM J. Matrix Anal. Appl. 35, 904\u2013930 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR8","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1137\/140993211","volume":"36","author":"CJ Delgado","year":"2015","unstructured":"Delgado, C. J., Pe\u00f1a, J. M.: Accurate computations with collocation matrices of q-Bernstein polynomials. SIAM J. Matrix Anal. Appl. 36, 880\u2013893 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR9","doi-asserted-by":"publisher","first-page":"562","DOI":"10.1137\/S0895479897328716","volume":"21","author":"J Demmel","year":"1999","unstructured":"Demmel, J.: Accurate singular value decompositions of structured matrices. SIAM J. Matrix Anal. Appl. 21, 562\u2013580 (1999)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/S0024-3795(99)00134-2","volume":"299","author":"CJ Demmel","year":"1999","unstructured":"Demmel, C. J., Gu, M., Eisenstat, S., Slapni\u010dar, I., Veseli\u0107, K., Drma\u010d, Z.: Computing the singular value decomposition with high relative accuracy. Linear Algebra Appl. 299, 21\u201380 (1999)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR11","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1017\/S0962492906350015","volume":"17","author":"CJ Demmel","year":"2008","unstructured":"Demmel, C. J., Dumitriu, I., Holtz, O., Koev, P.: Accurate and efficient expression evaluation and linear algebra. Acta Numer. 17, 87\u2013145 (2008)","journal-title":"Acta Numer."},{"key":"9898_CR12","doi-asserted-by":"publisher","first-page":"1096","DOI":"10.1093\/imanum\/drr023","volume":"32","author":"FM Dopico","year":"2012","unstructured":"Dopico, F.M., Molera, J.M.: Accurate solution of structured linear systems via rank-revealing decompositions. IMA J. Numer Anal. 32, 1096\u20131116 (2012)","journal-title":"IMA J. Numer Anal."},{"key":"9898_CR13","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1137\/S089547980139371X","volume":"25","author":"CFM Dopico","year":"2003","unstructured":"Dopico, C. F. M., Molera, J. M., Moro, J.: An orthogonal high relative accuracy algorithm for the symmetric eigenproblem. SIAM J. Matrix Anal. Appl. 25, 301\u2013351 (2003)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR14","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s00211-015-0779-5","volume":"134","author":"CFM Dopico","year":"2016","unstructured":"Dopico, C. F. M., Pom\u00e9s, K.: Structured eigenvalue condition numbers for parameterized quasiseparable matrices. Numer. Math. 134, 473\u2013512 (2016)","journal-title":"Numer. Math."},{"key":"9898_CR15","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0024-3795(92)90226-Z","volume":"165","author":"CM Gasca","year":"1992","unstructured":"Gasca, C. M., Pe\u00f1a, J. M.: Total positivity and Neville elimination. Linear Algebra Appl. 165, 25\u201344 (1992)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR16","doi-asserted-by":"crossref","unstructured":"Gasca, C. M., Pe\u00f1a, J. M.: On factorizations of totally positive matrices, in Total positivity and its Applications. Kluwer Academic Publishers, Dordrecht (1996)","DOI":"10.1007\/978-94-015-8674-0_7"},{"key":"9898_CR17","doi-asserted-by":"publisher","first-page":"1229","DOI":"10.1007\/s10915-017-0584-7","volume":"75","author":"R Huang","year":"2018","unstructured":"Huang, R.: A periodic qd-type reduction for computing eigenvalues of structured matrix products to high relative accuracy. J. Sci. Comput. 75, 1229\u20131261 (2018)","journal-title":"J. Sci. Comput."},{"key":"9898_CR18","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1016\/j.apnum.2019.08.001","volume":"146","author":"R Huang","year":"2019","unstructured":"Huang, R.: Accurate solutions of weighted least squares problems associated with rank-structured matrices. Appl. Numer. Math. 146, 416\u2013435 (2019)","journal-title":"Appl. Numer. Math."},{"key":"9898_CR19","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/s10915-020-01182-4","volume":"82","author":"R Huang","year":"2020","unstructured":"Huang, R.: Accurate eigenvalues of some generalized sign regular matrices via relatively robust representations. J. Sci. Comput. 82, 78 (2020). https:\/\/doi.org\/10.1007\/s10915-020-01182-4","journal-title":"J. Sci. Comput."},{"key":"9898_CR20","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1090\/mcom\/3444","volume":"89","author":"CR Huang","year":"2020","unstructured":"Huang, C. R.: A qd-type method for computing generalized singular values of BF matrix pairs with sign regularity to high relative accuracy. Math. Comp. 89, 229\u2013252 (2020)","journal-title":"Math. Comp."},{"key":"9898_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S0895479803438225","volume":"27","author":"CP Koev","year":"2005","unstructured":"Koev, C. P.: Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J Matrix Anal. Appl. 27, 1\u201323 (2005)","journal-title":"SIAM J Matrix Anal. Appl."},{"key":"9898_CR22","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1137\/04061903X","volume":"29","author":"P Koev","year":"2007","unstructured":"Koev, P.: Accurate computations with totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 29, 731\u2013751 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9898_CR23","unstructured":"Koev, P. http:\/\/math.mit.edu\/~plamen\/software\/TNTool.html"},{"key":"9898_CR24","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1007\/s11425-015-5102-5","volume":"59","author":"QH Liu","year":"2016","unstructured":"Liu, Q.H., Li, X.X., Yan, J.: On the large time behavior of solutions for a class of time-dependent Hamilton-Jacobi equations. Sci. China Math. 59, 875\u2013890 (2016)","journal-title":"Sci. China Math."},{"key":"9898_CR25","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1016\/j.laa.2006.11.020","volume":"422","author":"CA Marco","year":"2007","unstructured":"Marco, C. A., Mart\u00ednez, J. -J.: A fast and accurate algorithm for solving Bernstein-Vandermonde linear systems. Linear Algebra Appl. 422, 616\u2013628 (2007)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR26","doi-asserted-by":"publisher","first-page":"2894","DOI":"10.1016\/j.laa.2009.12.034","volume":"432","author":"CA Marco","year":"2010","unstructured":"Marco, C. A., Mart\u00ednez, J. -J.: Accurate computations with Said-Ball-Vandemonde matrices. Linear Algebra Appl. 432, 2894\u20132908 (2010)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR27","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1016\/j.laa.2010.06.031","volume":"433","author":"CA Marco","year":"2010","unstructured":"Marco, C. A., Mart\u00ednez, J. -J.: Polynomial least squares fitting in the Bernstein basis. Linear Algebra Appl. 433, 1254\u20131264 (2010)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR28","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.laa.2016.12.003","volume":"517","author":"A Marco","year":"2017","unstructured":"Marco, A., Mart\u00ednez, J-J., Pe\u00f1a, J.M.: Accurate bidiagonal decomposition of totally positive Cauchy-Vandermonde matrices and applications. Linear Algebra Appl. 517, 63\u201384 (2017)","journal-title":"Linear Algebra Appl."},{"key":"9898_CR29","doi-asserted-by":"crossref","DOI":"10.1353\/book.3417","volume-title":"Matrix Computations and Semiseparable Matrices. Vol. I: Linear systems","author":"CR Vandebril","year":"2008","unstructured":"Vandebril, C. R., Van Barel, M., Mastronardi, N.: Matrix Computations and Semiseparable Matrices. Vol. I: Linear systems. Johns Hopkins University Press, Baltimore (2008)"},{"key":"9898_CR30","doi-asserted-by":"publisher","first-page":"2195","DOI":"10.1090\/S0025-5718-08-02112-1","volume":"77","author":"CQ Ye","year":"2008","unstructured":"Ye, C. Q.: Computing singular values of diagonally dominant matrices to high relative accuracy. Math. Comp. 77, 2195\u20132230 (2008)","journal-title":"Math. Comp."},{"key":"9898_CR31","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1137\/060676349","volume":"31","author":"Q Ye","year":"2009","unstructured":"Ye, Q.: Relative perturbation bounds for eigenvalues of symmetric positive definite diagonally dominant matrices. SIAM J. Matrix Anal. Appl. 31, 11\u201317 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-021-09898-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-021-09898-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-021-09898-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T05:03:56Z","timestamp":1725771836000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-021-09898-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,10]]},"references-count":31,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["9898"],"URL":"https:\/\/doi.org\/10.1007\/s10444-021-09898-z","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,10]]},"assertion":[{"value":"14 April 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 August 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"73"}}