{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T11:10:55Z","timestamp":1772017855859,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T00:00:00Z","timestamp":1589932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671187"],"award-info":[{"award-number":["11671187"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01171-1","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T12:02:55Z","timestamp":1589976175000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Properties of a class of perturbed Toeplitz periodic tridiagonal matrices"],"prefix":"10.1007","volume":"39","author":[{"given":"Yaru","family":"Fu","sequence":"first","affiliation":[]},{"given":"Xiaoyu","family":"Jiang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9521-9835","authenticated-orcid":false,"given":"Zhaolin","family":"Jiang","sequence":"additional","affiliation":[]},{"given":"Seongtae","family":"Jhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,5,20]]},"reference":[{"issue":"1","key":"1171_CR1","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF02198300","volume":"10","author":"M Alfaro","year":"1995","unstructured":"Alfaro M, Montaner JM (1995) On five-diagonal Toeplitz matrices and orthogonal polynomials on the unit circle. Numer Algorithms 10(1):137\u2013153","journal-title":"Numer Algorithms"},{"issue":"1","key":"1171_CR2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1137\/1019002","volume":"19","author":"A Bj\u00f6rck","year":"1977","unstructured":"Bj\u00f6rck A, Golub GH (1977) Eigenproblems for matrices mssociated with periodic boundary conditions. SIAM Rev 19(1):5\u201316","journal-title":"SIAM Rev"},{"issue":"4","key":"1171_CR3","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1080\/00207160210941","volume":"79","author":"MM Chawla","year":"2002","unstructured":"Chawla MM, Khazal R (2002) A parallel elimination method for \u2018Periodic\u2019 tridiagonal systems. Int J Comput Math 79(4):473\u2013484","journal-title":"Int J Comput Math"},{"key":"1171_CR4","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1080\/00207169208804121","volume":"45","author":"MM Chawla","year":"1992","unstructured":"Chawla MM, Passi K, Shivakumar PN (1992) A fast parallel algorithm for the solution of tridiagonal linear systems. Int J Comput Math 45:113\u2013121","journal-title":"Int J Comput Math"},{"issue":"2","key":"1171_CR5","first-page":"691","volume":"161","author":"MEA El-Mikkawy","year":"2005","unstructured":"El-Mikkawy MEA (2005) A new computational algorithm for solving periodic tri-diagonal linear systems. Appl Math Comput 161(2):691\u2013696","journal-title":"Appl Math Comput"},{"key":"1171_CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.jmaa.2008.04.002","volume":"345","author":"MA El-Shehawey","year":"2008","unstructured":"El-Shehawey MA, El-Shreef GA, Al-Henawy AS (2008) Analytical inversion of general periodic tridiagonal matrices. J Math Anal Appl 345:123\u2013134","journal-title":"J Math Anal Appl"},{"key":"1171_CR7","volume-title":"Matrix computations","author":"GH Golub","year":"1996","unstructured":"Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. The John Hopkins University Press, Baltimore","edition":"3"},{"key":"1171_CR8","first-page":"207","volume":"335","author":"T Hopkins","year":"2018","unstructured":"Hopkins T, K\u0131l\u0131\u00e7 E (2018) An analytical approach: explicit inverses of periodic tridiagonal matrices. J Math Anal Appl 335:207\u2013226","journal-title":"J Math Anal Appl"},{"key":"1171_CR9","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1023\/A:1019109222477","volume":"25","author":"F Iachello","year":"1999","unstructured":"Iachello F, Del Sol Mesa A (1999) A class of exactly solvable matrix models. J Math Chem 25:345\u2013363","journal-title":"J Math Chem"},{"issue":"8","key":"1171_CR10","doi-asserted-by":"crossref","first-page":"2222","DOI":"10.1007\/s10910-014-0378-1","volume":"52","author":"JT Jia","year":"2014","unstructured":"Jia JT, Kong QX (2014) A symbolic algorithm for periodic tridiagonal systems of equations. J Math Chem 52(8):2222\u20132233","journal-title":"J Math Chem"},{"key":"1171_CR11","unstructured":"Maplesoft (2017) Maplesoft, a division of Waterloo Maple Inc., Maple, Waterloo"},{"key":"1171_CR12","volume-title":"Discrete mathematics and its applications","author":"KH Rosen","year":"2011","unstructured":"Rosen KH (2011) Discrete mathematics and its applications, 6th edn. McGraw-Hill, New York","edition":"6"},{"issue":"2","key":"1171_CR13","first-page":"850","volume":"202","author":"T Sogabe","year":"2008","unstructured":"Sogabe T (2008) New algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems. Appl Math Comput 202(2):850\u2013856","journal-title":"Appl Math Comput"},{"key":"1171_CR14","volume-title":"Fibonacci and Lucas numbers with applications","author":"K Thomas","year":"2001","unstructured":"Thomas K (2001) Fibonacci and Lucas numbers with applications. Wiley, New York"},{"issue":"6","key":"1171_CR15","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1016\/j.parco.2005.01.002","volume":"31","author":"J Verkaik","year":"2005","unstructured":"Verkaik J, Lin HX (2005) A class of novel parallel algorithms for the solution of tridiagonal systems. Parallel Comput 31(6):563\u2013587","journal-title":"Parallel Comput"},{"key":"1171_CR16","unstructured":"Wolfram Research, Inc. (2017) Mathematica, Version 11.2, Champaign"},{"issue":"1","key":"1171_CR17","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/BF01164461","volume":"14","author":"YJ Ye","year":"1993","unstructured":"Ye YJ, Ladik J (1993) The extended negative factor counting method for tridiagonal block matrices with cross links. J Math Chem 14(1):121\u2013139","journal-title":"J Math Chem"},{"key":"1171_CR18","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1017\/S1446181108000102","volume":"49","author":"WC Yueh","year":"2008","unstructured":"Yueh WC, Cheng SS (2008) Explicit eigenvalues and inverses of tridiagonal Toeplitz matrices with four perturbed corners. ANZIAM J 49:361\u2013387","journal-title":"ANZIAM J"},{"key":"1171_CR19","volume-title":"The Schur complement and its applications","author":"FZ Zhang","year":"2006","unstructured":"Zhang FZ (2006) The Schur complement and its applications. Springer Science & Business Media, New York"},{"key":"1171_CR20","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1023\/A:1018852612649","volume":"28","author":"M Znojil","year":"2000","unstructured":"Znojil M (2000) Perturbation method with triangular propagators and anharmonicities of intermediate strength. J Math Chem 28:139\u2013167","journal-title":"J Math Chem"},{"key":"1171_CR21","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1515\/spma-2018-0017","volume":"6","author":"BS Zuo","year":"2018","unstructured":"Zuo BS, Jiang ZL, Fu DQ (2018) Determinants and inverses of Ppoeplitz and Ppankel matrices. Spec Matrices 6:201\u2013215","journal-title":"Spec Matrices"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01171-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01171-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01171-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,20]],"date-time":"2021-05-20T07:34:01Z","timestamp":1621496041000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01171-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,20]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1171"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01171-1","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,20]]},"assertion":[{"value":"20 January 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 April 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 May 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"146"}}