{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:40:15Z","timestamp":1740123615915,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T00:00:00Z","timestamp":1647388800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T00:00:00Z","timestamp":1647388800000},"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":["J Supercomput"],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1007\/s11227-022-04373-y","type":"journal-article","created":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T14:04:03Z","timestamp":1647439443000},"page":"13245-13275","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Taylor polynomials as an estimator for certain toeplitz matrices"],"prefix":"10.1007","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8820-9858","authenticated-orcid":false,"given":"Michael","family":"Kapralos","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,16]]},"reference":[{"unstructured":"Advanpix L Multiprecision computing toolbox for matlab, yokohama, japan, 2008\u20132020","key":"4373_CR1"},{"key":"4373_CR2","first-page":"512","volume":"236","author":"S Belhaj","year":"2014","unstructured":"Belhaj S, Dridi M (2014) A note on computing the inverse of a triangular toeplitz matrix. Appl Math Comput 236:512\u2013523","journal-title":"Appl Math Comput"},{"issue":"2","key":"4373_CR3","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1137\/0213019","volume":"13","author":"D Bini","year":"1984","unstructured":"Bini D (1984) Parallel solution of certain Toeplitz linear systems. SIAM J Comput 13(2):268\u2013276","journal-title":"SIAM J Comput"},{"issue":"3","key":"4373_CR4","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/0885-064X(86)90001-4","volume":"2","author":"D Bini","year":"1986","unstructured":"Bini D, Pan V (1986) Polynomial division and its computational complexity. J Complex 2(3):179\u2013203. https:\/\/doi.org\/10.1016\/0885-064X(86)90001-4","journal-title":"J Complex"},{"issue":"3","key":"4373_CR5","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1137\/0222041","volume":"22","author":"D Bini","year":"1993","unstructured":"Bini D, Pan V (1993) Improved parallel polynomial division. SIAM J Comput 22(3):617\u2013626","journal-title":"SIAM J Comput"},{"doi-asserted-by":"crossref","unstructured":"Bini D, Pan V (1993) Parallel computations with toeplitz-like and hankel-like matrices. In: Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation, pp 193\u2013200. ACM (1993)","key":"4373_CR6","DOI":"10.1145\/164081.164124"},{"doi-asserted-by":"crossref","unstructured":"Bini D, Pan VY (1994) Polynomial and matrix computations. Volume 1: Fundamental algorithms. Progress in Theoretical Computer Science. Birkh\u00e4user Verlag, Boston-Basel-Berlin-Stuttgart","key":"4373_CR7","DOI":"10.1007\/978-1-4612-0265-3_1"},{"doi-asserted-by":"crossref","unstructured":"Bini DA, Codevico G, Van Barel M (2003) Solving toeplitz least squares problems by means of newton\u2019s iteration. Numerical Algorithms 33(1\u20134):93\u2013103","key":"4373_CR8","DOI":"10.1023\/A:1025543417700"},{"issue":"3","key":"4373_CR9","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1137\/S0895479897324585","volume":"20","author":"DA Bini","year":"1999","unstructured":"Bini DA, Meini B (1999) Effective methods for solving banded toeplitz systems. SIAM J Matrix Anal Appl 20(3):700\u2013719","journal-title":"SIAM J Matrix Anal Appl"},{"key":"4373_CR10","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1090\/conm\/281\/04659","volume":"281","author":"DA Bini","year":"2001","unstructured":"Bini DA, Meini B (2001) Approximate displacement rank and applications. Contemp Math 281:215\u2013232","journal-title":"Contemp Math"},{"issue":"1","key":"4373_CR11","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s11075-008-9253-0","volume":"51","author":"DA Bini","year":"2009","unstructured":"Bini DA, Meini B (2009) The cyclic reduction algorithm: from poisson equation to stochastic processes and beyond. Numer Algorithms 51(1):23\u201360","journal-title":"Numer Algorithms"},{"issue":"12","key":"4373_CR12","doi-asserted-by":"publisher","first-page":"4760","DOI":"10.1016\/j.laa.2013.02.020","volume":"438","author":"A B\u00f6ttcher","year":"2013","unstructured":"B\u00f6ttcher A, Halwass M (2013) Wiener-hopf and spectral factorization of real polynomials by newton\u2019s method. Linear Algebra Appl 438(12):4760\u20134805","journal-title":"Linear Algebra Appl"},{"key":"4373_CR13","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/j.jpdc.2018.04.017","volume":"119","author":"E Chow","year":"2018","unstructured":"Chow E, Anzt H, Scott J, Dongarra J (2018) Using jacobi iterations and blocking for solving sparse triangular systems in incomplete factorization preconditioning. J Parallel Distrib Comput 119:219\u2013230","journal-title":"J Parallel Distrib Comput"},{"key":"4373_CR14","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1109\/TAC.1984.1103499","volume":"29","author":"D Commenges","year":"1984","unstructured":"Commenges D, Monsion M (1984) Fast inversion of triangular toeplitz matrices. IEEE Trans Autom Control 29:250\u2013251","journal-title":"IEEE Trans Autom Control"},{"issue":"90","key":"4373_CR15","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/S0025-5718-1965-0178586-1","volume":"19","author":"JW Cooley","year":"1965","unstructured":"Cooley JW, Tukey JW (1965) An algorithm for the machine calculation of complex fourier series. Math Comput 19(90):297\u2013301","journal-title":"Math Comput"},{"issue":"2","key":"4373_CR16","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1137\/0902020","volume":"2","author":"J Grcar","year":"1981","unstructured":"Grcar J, Sameh A (1981) On certain parallel toeplitz linear system solvers. SIAM J Sci Stat Comput 2(2):238\u2013256","journal-title":"SIAM J Sci Stat Comput"},{"doi-asserted-by":"crossref","unstructured":"van der Hoeven J (2010) Newton\u2019s method and fft trading. J Symb Comput 45(8):857\u2013878","key":"4373_CR17","DOI":"10.1016\/j.jsc.2010.03.005"},{"unstructured":"Huang J, Huang TZ, Belhaj S (2013) Scaling bini\u2019s algorithm for fast inversion of triangular toeplitz matrices. J Comput Anal Appl 15(5):858\u2013867","key":"4373_CR18"},{"key":"4373_CR19","volume-title":"Analysis of numerical methods","author":"E Isaacson","year":"1966","unstructured":"Isaacson E, Keller HB (1966) Analysis of numerical methods. Wiley, United States"},{"unstructured":"Kapralos (2021) Estimator. Internet Website, Last accessed 10\/21\/2021. Https:\/\/github.com\/BDDTT\/Estimator","key":"4373_CR20"},{"doi-asserted-by":"crossref","unstructured":"Kapralos M, Wolinetz A, Murphy BJ (2016) Parallel solution of diagonally dominant banded triangular toeplitz systems using taylor polynomials. In: 18th IEEE International Conference on High Performance Computing and Communications; 14th IEEE International Conference on Smart City; 2nd IEEE International Conference on Data Science and Systems, HPCC\/SmartCity\/DSS 2016, Sydney, Australia, December 12-14, 2016, pp 601\u2013607","key":"4373_CR21","DOI":"10.1109\/HPCC-SmartCity-DSS.2016.0090"},{"issue":"8","key":"4373_CR22","doi-asserted-by":"publisher","first-page":"1091","DOI":"10.1016\/S0167-8191(96)00028-2","volume":"22","author":"JL Larriba-Pey","year":"1996","unstructured":"Larriba-Pey JL, Navarro JJ, Jorba A, Roig O (1996) Review of general and toeplitz vector bidiagonal solvers. Parallel Comput 22(8):1091\u20131126","journal-title":"Parallel Comput"},{"issue":"2","key":"4373_CR23","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.tcs.2004.01.005","volume":"315","author":"FR Lin","year":"2004","unstructured":"Lin FR, Ching WK, Ng MK (2004) Fast inversion of triangular toeplitz matrices. Theoret Comput Sci 315(2):511\u2013523","journal-title":"Theoret Comput Sci"},{"issue":"1","key":"4373_CR24","first-page":"327","volume":"206","author":"XG Lv","year":"2008","unstructured":"Lv XG, Huang TZ, Le J (2008) A note on computing the inverse and the determinant of a pentadiagonal toeplitz matrix. Appl Math Comput 206(1):327\u2013331","journal-title":"Appl Math Comput"},{"doi-asserted-by":"crossref","unstructured":"Malyshev A, Sadkane M (2014) Fast solution of unsymmetric banded toeplitz systems by means of spectral factorizations and woodbury\u2019s formula. Numer Linear Algebra Appl 21(1):13\u201323","key":"4373_CR25","DOI":"10.1002\/nla.1853"},{"issue":"2","key":"4373_CR26","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.cam.2006.12.001","volume":"212","author":"JM McNally","year":"2008","unstructured":"McNally JM, Garey L, Shaw R (2008) A communication-less parallel algorithm for tridiagonal toeplitz systems. J Comput Appl Math 212(2):260\u2013271","journal-title":"J Comput Appl Math"},{"key":"4373_CR27","first-page":"321","volume":"6885","author":"BJ Murphy","year":"2011","unstructured":"Murphy BJ (2011) Acceleration of the inversion of triangular toeplitz matrices and polynomial division. Comput Algebra Sci Comput: Lect Notes Comput Sci 6885:321\u2013332","journal-title":"Comput Algebra Sci Comput: Lect Notes Comput Sci"},{"doi-asserted-by":"crossref","unstructured":"Pan VY, Branham S, Rosholt RE, Zheng AL (1999) Newton\u2019s iteration for structured matrices. In: Fast reliable algorithms for matrices with structure, pp. 189\u2013210. SIAM","key":"4373_CR28","DOI":"10.1137\/1.9781611971354.ch7"},{"doi-asserted-by":"crossref","unstructured":"Pan VY, Rami Y, Wang X (2002) Structured matrices and newton\u2019s iteration: unified approach. Linear Algebra Appl 343:233\u2013265","key":"4373_CR29","DOI":"10.1016\/S0024-3795(01)00336-6"},{"key":"4373_CR30","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1016\/S0020-0190(00)00044-2","volume":"74","author":"A Sch\u00f6nhage","year":"2000","unstructured":"Sch\u00f6nhage A (2000) Variations on computing reciprocals of power series. Inf Process Lett 74:41\u201346","journal-title":"Inf Process Lett"},{"issue":"1\u20132","key":"4373_CR31","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/BF02242389","volume":"10","author":"M Sieveking","year":"1972","unstructured":"Sieveking M (1972) An algorithm for division of power series. Computing 10(1\u20132):153\u2013156","journal-title":"Computing"},{"issue":"1","key":"4373_CR32","first-page":"1","volume":"1","author":"P Stpiczy\u0144ski","year":"2015","unstructured":"Stpiczy\u0144ski P (2015) Fast solver for toeplitz bidiagonal systems of linear equations. Ann Univ Mariae Curie-Sklodowska, sectio AI-Inform 1(1):1\u20137","journal-title":"Ann Univ Mariae Curie-Sklodowska, sectio AI-Inform"},{"unstructured":"Sun XH, Moitra S (1996) A fast parallel tridiagonal algorithm for a class of CFD applications. NASA Langley Technical Report Server","key":"4373_CR33"},{"issue":"3","key":"4373_CR34","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1137\/0112045","volume":"12","author":"WF Trench","year":"1964","unstructured":"Trench WF (1964) An algorithm for the inversion of finite toeplitz matrices. J Soc Ind Appl Math 12(3):515\u2013522","journal-title":"J Soc Ind Appl Math"},{"issue":"128","key":"4373_CR35","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1090\/S0025-5718-1974-0347066-8","volume":"28","author":"WF Trench","year":"1974","unstructured":"Trench WF (1974) Inversion of toeplitz band matrices. Math Comput 28(128):1089\u20131095","journal-title":"Math Comput"},{"issue":"4","key":"4373_CR36","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1137\/0606054","volume":"6","author":"WF Trench","year":"1985","unstructured":"Trench WF (1985) Explicit inversion formulas for toeplitz band matrices. SIAM J Algebr Discrete Methods 6(4):546\u2013554","journal-title":"SIAM J Algebr Discrete Methods"},{"key":"4373_CR37","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1016\/S0024-3795(87)90311-9","volume":"93","author":"WF Trench","year":"1987","unstructured":"Trench WF (1987) A note on solving nearly triangular toeplitz systems. Linear Algebra Appl 93:57\u201365","journal-title":"Linear Algebra Appl"},{"unstructured":"Wang X, Huang Y (2012) A fast algorithm for inversion of real lower triangular toeplitz matrices. J Comput Anal Appl 14(1)","key":"4373_CR38"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04373-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-022-04373-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-04373-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T14:10:27Z","timestamp":1656943827000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-022-04373-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,16]]},"references-count":38,"journal-issue":{"issue":"11","published-print":{"date-parts":[[2022,7]]}},"alternative-id":["4373"],"URL":"https:\/\/doi.org\/10.1007\/s11227-022-04373-y","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2022,3,16]]},"assertion":[{"value":"12 February 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}