A locally convergent continuous-time algorithm to find all the roots of a time-varying polynomial
In this technical communique, a locally convergent continuous-time model for the Durand–Kerner method is proposed to simultaneously determine all the roots of a time-varying polynomial. The effectiveness of this method is demonstrated through its application to a benchmark example.
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| Vydáno v: | Automatica (Oxford) Ročník 131; s. 109681 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier Ltd
01.09.2021
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | In this technical communique, a locally convergent continuous-time model for the Durand–Kerner method is proposed to simultaneously determine all the roots of a time-varying polynomial. The effectiveness of this method is demonstrated through its application to a benchmark example. |
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| AbstractList | In this technical communique, a locally convergent continuous-time model for the Durand–Kerner method is proposed to simultaneously determine all the roots of a time-varying polynomial. The effectiveness of this method is demonstrated through its application to a benchmark example. |
| ArticleNumber | 109681 |
| Author | Tornambè, Antonio Menini, Laura Possieri, Corrado |
| Author_xml | – sequence: 1 givenname: Laura surname: Menini fullname: Menini, Laura email: laura.menini@uniroma2.it organization: Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, 00133, Roma, Italy – sequence: 2 givenname: Corrado surname: Possieri fullname: Possieri, Corrado email: corrado.possieri@iasi.cnr.it organization: Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche (IASI-CNR), 00185 Roma, Italy – sequence: 3 givenname: Antonio surname: Tornambè fullname: Tornambè, Antonio email: tornambe@disp.uniroma2.it organization: Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, 00133, Roma, Italy |
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| Cites_doi | 10.1016/j.automatica.2019.01.003 10.1016/j.automatica.2017.12.021 10.1006/jmaa.1999.6453 10.1007/s11075-015-0088-1 10.1109/TAC.2015.2449811 10.1080/00036819908840791 10.1007/BF02162564 10.1109/T-AIEE.1950.5060121 10.1007/s11075-010-9410-0 10.1016/0167-6911(91)90116-V 10.1080/01630560008816971 |
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| Keywords | Polynomial methods Lyapunov stability Convergence of numerical methods Roots |
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| References | Evans (b6) 1950; 69 Helmke, Moore (b9) 2012 Riaza, Zufiria (b20) 1999; 236 Durand (b4) 1961 Butcher, Goodwin (b2) 2008 Eberly (b5) 2006 Muehlebach, Jordan (b16) 2019 Nicosia, Tornambe, Valigi (b18) 1991; 16 Menini, Possieri, Tornambe (b15) 2019; 104 Saupe (b21) 1988 Schropp, Singer (b22) 2000; 21 Menini, Possieri, Tornambe (b14) 2018; 89 Macdonald (b13) 1998 Zhang, Xiao, Ruan, Li (b24) 2011; 57 Kovesi (b12) 2003; 2003 Airapetyan (b1) 1999; 73 Jin, Zhang (b10) 2016; 73 Franca, Robinson, Vidal (b7) 2018 Kerner (b11) 1966; 8 Cox, Little, O’Shea (b3) 2015 Varagnolo, Zanella, Cenedese, Pillonetto, Schenato (b23) 2015; 61 Fritzsche, Grauert (b8) 2012 Nedialkov (b17) 2006 Parusinski, Rainer (b19) 2016; 16 Riaza (10.1016/j.automatica.2021.109681_b20) 1999; 236 Fritzsche (10.1016/j.automatica.2021.109681_b8) 2012 Nedialkov (10.1016/j.automatica.2021.109681_b17) 2006 Franca (10.1016/j.automatica.2021.109681_b7) 2018 Helmke (10.1016/j.automatica.2021.109681_b9) 2012 Muehlebach (10.1016/j.automatica.2021.109681_b16) 2019 Menini (10.1016/j.automatica.2021.109681_b15) 2019; 104 Nicosia (10.1016/j.automatica.2021.109681_b18) 1991; 16 Durand (10.1016/j.automatica.2021.109681_b4) 1961 Jin (10.1016/j.automatica.2021.109681_b10) 2016; 73 Macdonald (10.1016/j.automatica.2021.109681_b13) 1998 Kerner (10.1016/j.automatica.2021.109681_b11) 1966; 8 Airapetyan (10.1016/j.automatica.2021.109681_b1) 1999; 73 Butcher (10.1016/j.automatica.2021.109681_b2) 2008 Menini (10.1016/j.automatica.2021.109681_b14) 2018; 89 Zhang (10.1016/j.automatica.2021.109681_b24) 2011; 57 Eberly (10.1016/j.automatica.2021.109681_b5) 2006 Evans (10.1016/j.automatica.2021.109681_b6) 1950; 69 Saupe (10.1016/j.automatica.2021.109681_b21) 1988 Varagnolo (10.1016/j.automatica.2021.109681_b23) 2015; 61 Cox (10.1016/j.automatica.2021.109681_b3) 2015 Kovesi (10.1016/j.automatica.2021.109681_b12) 2003; 2003 Parusinski (10.1016/j.automatica.2021.109681_b19) 2016; 16 Schropp (10.1016/j.automatica.2021.109681_b22) 2000; 21 |
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| SubjectTerms | Convergence of numerical methods Lyapunov stability Polynomial methods Roots |
| Title | A locally convergent continuous-time algorithm to find all the roots of a time-varying polynomial |
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