{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:40Z","timestamp":1740123940415,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T00:00:00Z","timestamp":1655251200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007041","name":"Universidad de Zaragoza","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007041","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2022,8]]},"abstract":"Abstract<\/jats:title>The total positivity of collocation, Wronskian and Gram matrices corresponding to bases of the form (e<\/jats:italic>\u03bb<\/jats:italic>t<\/jats:italic><\/jats:sup>,t<\/jats:italic>e<\/jats:italic>\u03bb<\/jats:italic>t<\/jats:italic><\/jats:sup>,\u2026,t<\/jats:italic>n<\/jats:italic><\/jats:sup>e<\/jats:italic>\u03bb<\/jats:italic>t<\/jats:italic><\/jats:sup>) is analyzed. A bidiagonal decomposition providing the accurate numerical resolution of algebraic linear problems with these matrices is derived. The numerical experimentation confirms the accuracy of the proposed methods.<\/jats:p>","DOI":"10.1007\/s10444-022-09954-2","type":"journal-article","created":{"date-parts":[[2022,6,15]],"date-time":"2022-06-15T14:02:56Z","timestamp":1655301776000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Accurate computations with matrices related to bases {tie\u03bbt}"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1101-6230","authenticated-orcid":false,"given":"E.","family":"Mainar","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1340-0666","authenticated-orcid":false,"given":"J. M.","family":"Pe\u00f1a","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9130-0794","authenticated-orcid":false,"given":"B.","family":"Rubio","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,6,15]]},"reference":[{"key":"9954_CR1","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.cam.2011.12.007","volume":"252","author":"P Alonso","year":"2013","unstructured":"Alonso, P., Delgado, J., Gallego, R., Pe\u00f1a, J. M.: Conditioning and accurate computations with Pascal matrices. J. Comput. Appl. Math. 252, 21\u201326 (2013)","journal-title":"J. Comput. Appl. Math."},{"key":"9954_CR2","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/0024-3795(87)90313-2","volume":"90","author":"T Ando","year":"1987","unstructured":"Ando, T.: Totally positive matrices. Linear Algebra Appl. 90, 165\u2013219 (1987)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR3","first-page":"4354","volume":"219","author":"J Delgado","year":"2013","unstructured":"Delgado, J., Pe\u00f1a, J.M.: Accurate computations with collocation matrices of rational bases. Appl. Math. Comput. 219, 4354\u20134364 (2013)","journal-title":"Appl. Math. Comput."},{"key":"9954_CR4","first-page":"253","volume":"236","author":"J Delgado","year":"2014","unstructured":"Delgado, J., Pe\u00f1a, J. M.: Fast and accurate algorithms for Jacobi-Stirling matrices. Appl. Math. Comput. 236, 253\u2013259 (2014)","journal-title":"Appl. Math. Comput."},{"key":"9954_CR5","doi-asserted-by":"publisher","first-page":"e2217","DOI":"10.1002\/nla.2217","volume":"26","author":"J Delgado","year":"2019","unstructured":"Delgado, J., Orera, H., Pe\u00f1a, J. M.: Accurate computations with Laguerre matrices. Numer Linear Algebra Appl. 26, e2217 (2019). 10 pp.","journal-title":"Numer Linear Algebra Appl."},{"key":"9954_CR6","doi-asserted-by":"publisher","first-page":"1264","DOI":"10.1007\/s10915-019-00975-6","volume":"80","author":"J Delgado","year":"2019","unstructured":"Delgado, J., Orera, H., Pe\u00f1a, J. M.: Accurate algorithms for Bessel matrices. J. Sci. Comput. 80, 1264\u20131278 (2019)","journal-title":"J. Sci. Comput."},{"key":"9954_CR7","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1137\/S0895479804440335","volume":"27","author":"J Demmel","year":"2005","unstructured":"Demmel, J., Koev, P.: The accurate and efficient solution of a totally positive generalized Vandermonde linear system. SIAM J. Matrix Anal. Appl. 27, 42\u201352 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"9954_CR8","doi-asserted-by":"publisher","DOI":"10.23943\/princeton\/9780691121574.001.0001","volume-title":"Totally Nonnegative Matrices","author":"SM Fallat","year":"2011","unstructured":"Fallat, S.M., Johnson, C.R.: Totally Nonnegative Matrices. Princeton University Press, Princeton (2011). Princeton Series in Applied Mathematics"},{"key":"9954_CR9","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0024-3795(93)90431-M","volume":"183","author":"T Finck","year":"1993","unstructured":"Finck, T., Heinig, G., Rost, K.: An inversion formula and fast algorithms for Cauchy-Vandermonde matrices. Linear Algebra Appl. 183, 179\u2013191 (1993)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR10","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/0024-3795(92)90226-Z","volume":"165","author":"M Gasca","year":"1992","unstructured":"Gasca, M., Pe\u00f1a, J. M.: Total positivity and Neville elimination. Linear Algebra Appl. 165, 25\u201344 (1992)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR11","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0024-3795(94)90183-X","volume":"202","author":"M Gasca","year":"1994","unstructured":"Gasca, M., Pe\u00f1a, J. M.: A matricial description of Neville elimination with applications to total positivity. Linear Algebra Appl. 202, 33\u201353 (1994)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR12","doi-asserted-by":"crossref","unstructured":"Gasca, M., Pe\u00f1a, J. M.: On factorizations of totally positive matrices. In: Gasca, M., Micchelli, C. A. (eds.) Total Positivity and Its Applications, pp 109\u2013130. Kluver Academic Publishers, Dordrecht (1996)","DOI":"10.1007\/978-94-015-8674-0_7"},{"key":"9954_CR13","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/0024-3795(87)90313-2","volume":"90","author":"R Hartwig","year":"1987","unstructured":"Hartwig, R.: Applications of the Wronskian and Gram matrices of $\\{ t^{i} e^{{\\lambda }_{k}t} \\}$. Linear Algebra Appl. 90, 165\u2013219 (1987)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR14","first-page":"47","volume":"73","author":"R Huang","year":"2021","unstructured":"Huang, R., Xue, J.: Accurate singular values of a class of parameterized negative matrices. Adv. Comput. Math. 73, 47 (2021). 2021","journal-title":"Adv. Comput. Math."},{"key":"9954_CR15","first-page":"229","volume":"43","author":"P Koev","year":"1982","unstructured":"Koev, P.: Accurate eigenvalues and SVDs of totally nonnegative matrices. SIAM J Matrix Anal. Appl. 43, 229\u2013241 (1982)","journal-title":"SIAM J Matrix Anal. Appl."},{"key":"9954_CR16","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":"9954_CR17","unstructured":"Koev, P.: Available online: http:\/\/www.math.mit.edu\/plamen\/software\/TNTool.html (2021). Accessed 24 Aug 2021"},{"key":"9954_CR18","doi-asserted-by":"publisher","first-page":"e2184","DOI":"10.1002\/nla.2184","volume":"25","author":"E Mainar","year":"2018","unstructured":"Mainar, E., Pe\u00f1a, J. M.: Accurate computations with collocation matrices of a general class of bases. Numer. Linear Algebra Appl. 25, e2184 (2018). 12 pp.","journal-title":"Numer. Linear Algebra Appl."},{"key":"9954_CR19","doi-asserted-by":"crossref","unstructured":"Mainar, E., Pe\u00f1a, J. M., Rubio, B.: Accurate bidiagonal decomposition of collocation matrices of weighted \u03c6 - transformed systems. Numer. Linear Algebra Appl., e2295 (2020)","DOI":"10.1002\/nla.2295"},{"key":"9954_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10092-020-00392-4","volume":"58","author":"E Mainar","year":"2021","unstructured":"Mainar, E., Pe\u00f1a, J. M., Rubio, B.: Accurate computations with Wronskian matrices. Calcolo 58, 1 (2021)","journal-title":"Calcolo"},{"key":"9954_CR21","doi-asserted-by":"crossref","unstructured":"Mainar, E., Pe\u00f1a, J. M., Rubio, B.: Accurate computations with collocation and Wronskian matrices of Jacobi polynomials. J. Sci. Comput., 87\u201377 (2021)","DOI":"10.1007\/s10915-021-01500-4"},{"key":"9954_CR22","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1016\/j.laa.2006.11.020","volume":"422","author":"A Marco","year":"2007","unstructured":"Marco, A., Mart\u00ednez, J.J.: A fast and accurate algorithm for solving BernsteinVandermonde linear systems. Linear Algebra Appl. 422, 616\u2013628 (2007)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR23","doi-asserted-by":"publisher","first-page":"2894","DOI":"10.1016\/j.laa.2009.12.034","volume":"432","author":"A Marco","year":"2010","unstructured":"Marco, A., Mart\u00ednez, J.J.: Accurate computations with Said-Ball-Vandermonde matrices. Linear Algebra Appl. 432, 2894\u20132908 (2010)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR24","doi-asserted-by":"publisher","first-page":"357","DOI":"10.13001\/1081-3810.1658","volume":"26","author":"A Marco","year":"2013","unstructured":"Marco, A., Mart\u00ednez, J.J.: Accurate computations with totally positive Bernstein-Vandermonde matrices. Electron J. Linear Algebra 26, 357\u2013380 (2013)","journal-title":"Electron J. Linear Algebra"},{"key":"9954_CR25","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.cam.2018.10.009","volume":"350","author":"A Marco","year":"2019","unstructured":"Marco, A., Mart\u00ednez, J. J.: Accurate computation of the Moore\u2013Penrose inverse of strictly totally positive matrices. J. Comput. Appl. Math. 350, 299\u2013308 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"9954_CR26","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\u2013Vandermonde matrices and applications. Linear Algebra Appl. 517, 63\u201384 (2017)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR27","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/S0024-3795(00)00124-5","volume":"315","author":"H Oruc","year":"2000","unstructured":"Oruc, H., Phillips, G.M.: Explicit factorization of the Vandermonde matrix. Linear Algebra Appl. 315, 113\u2013123 (2000)","journal-title":"Linear Algebra Appl."},{"key":"9954_CR28","volume-title":"Totally Positive Matrices. Cambridge Tracts in Mathematics, vol. 181","author":"A Pinkus","year":"2010","unstructured":"Pinkus, A.: Totally Positive Matrices. Cambridge Tracts in Mathematics, vol. 181. Cambridge University Press, Cambridge (2010)"},{"key":"9954_CR29","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s11075-019-00816-5","volume":"85","author":"Z Yang","year":"2020","unstructured":"Yang, Z., Huang, R., Zhu, W.: Accurate computations for eigenvalues of products of Cauchy-polynomial-Vandermonde matrices. Numer. Algor. 85, 329\u2013351 (2020)","journal-title":"Numer. Algor."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-09954-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-022-09954-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-022-09954-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T12:28:40Z","timestamp":1660048120000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-022-09954-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,15]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["9954"],"URL":"https:\/\/doi.org\/10.1007\/s10444-022-09954-2","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"type":"print","value":"1019-7168"},{"type":"electronic","value":"1572-9044"}],"subject":[],"published":{"date-parts":[[2022,6,15]]},"assertion":[{"value":"12 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"38"}}