A hybrid approach to joint spectral radius computation
In this paper we propose a new method to determine the joint spectral radius of a finite set of real matrices by verifying that a given family of candidates actually consists of spectrum maximizing products. Our algorithm aims at constructing a finite set-valued tree according to the approach of Möl...
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| Vydáno v: | Linear algebra and its applications |
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01.07.2025
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| Abstract | In this paper we propose a new method to determine the joint spectral radius of a finite set of real matrices by verifying that a given family of candidates actually consists of spectrum maximizing products. Our algorithm aims at constructing a finite set-valued tree according to the approach of Möller and Reif using a norm that is constructed in the spirit of the invariant polytope algorithm. This combines the broad range of applicability of the first algorithm with the efficiency of the latter.
•Novel approach for joint spectral radius computation.•Algorithm remains rigorous.•Algorithm has more general termination guarantees than classical invariant polytope algorithm. |
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| AbstractList | In this paper we propose a new method to determine the joint spectral radius of a finite set of real matrices by verifying that a given family of candidates actually consists of spectrum maximizing products. Our algorithm aims at constructing a finite set-valued tree according to the approach of Möller and Reif using a norm that is constructed in the spirit of the invariant polytope algorithm. This combines the broad range of applicability of the first algorithm with the efficiency of the latter.
•Novel approach for joint spectral radius computation.•Algorithm remains rigorous.•Algorithm has more general termination guarantees than classical invariant polytope algorithm. |
| Author | Reif, Ulrich Mejstrik, Thomas |
| Author_xml | – sequence: 1 givenname: Thomas orcidid: 0000-0003-2801-0828 surname: Mejstrik fullname: Mejstrik, Thomas email: thomas.mejstrik@gmx.at organization: NuHAG, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria – sequence: 2 givenname: Ulrich surname: Reif fullname: Reif, Ulrich email: reif@mathematik.tu-darmstadt.de organization: Fachbereich Mathematik, Technische Universität Darmstadt, Karolinenpl. 5, 64289, Darmstadt, Germany |
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| Cites_doi | 10.1016/j.laa.2007.12.027 10.1070/SM2000v191n03ABEH000464 10.1016/j.aim.2010.12.012 10.1137/040606818 10.1090/mcom/3856 10.1137/15M1006945 10.1016/0024-3795(95)90006-3 10.1137/0523059 10.1137/080715718 10.1016/0024-3795(92)90267-E 10.1016/j.laa.2014.08.009 10.1007/s10208-012-9121-0 10.1137/100817851 10.1016/j.laa.2007.07.009 10.1137/110855272 10.1016/0024-3795(93)00052-2 10.1137/S0895479801397846 10.1016/j.laa.2009.09.022 10.1090/S0894-0347-01-00378-2 10.1109/18.904557 10.1145/3408891 |
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| Keywords | Pseudo spectral radius Finite tree algorithm 15-04 Joint spectral radius Invariant polytope algorithm 90C90 Exact computation 15A60 15A18 |
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| References | Guglielmi, Overton (br0320) Moision, Orlitsky, Siegel (br0100) 2001; 47 Mejstrik (br0260) 2020; 46 Guglielmi, Overton (br0140) 2001; 32 Guglielmi, Protasov (br0170) 2024; 93 Berger, Yang (br0060) 1992; 166 Möller (br0270) 2015 Bousch, Mairesse (br0040) 2002; 15 Rota, Strang (br0310) 1960; 63 Guglielmi, Zennaro (br0190) 2007; 14 Möller, Reif (br0290) 2014; 463 Blondel, Theys, Vladimirov (br0050) 2003; 24 Guglielmi, Protasov (br0150) 2013; 13 Mengi (br0340) Daubechies, Lagarias (br0080) 1992; 23 Blondel, Tche (br0030) 2013; 64 Hare, Morris, Sidorov, Theys (br0220) 2011; 226 Lagarias, Wang (br0250) 1995; 214 Guglielmi, Zennaro (br0200) 2008; 428 Mejstrik (br0350) 2018 Guglielmi, Wirth, Zennaro (br0180) 2005; 27 Mengi (br0240) 2006 Guglielmi, Lubich (br0130) 2011; 49 Guglielmi, Protasov (br0160) 2016; 37 Hendrickx, Jungers, Vankeerberghen (br0330) 2011 Barabanov (br0020) 1988; 49 Jungers (br0230) 2009 Parrilo, Jadbabaie (br0300) 2008; 428 Cicone, Guglielmi, Serra-Capizzano, Zennaro (br0070) 2010; 432 Ahmadi, Jungers, Parrilo, Roozbehani (br0010) 2011; 52 Wright (br0360) 2002 Trefethen (br0090) 2005 Protasov (br0120) 2000; 191 Guglielmi, Zennaro (br0210) 2009; 31 Gurvits (br0110) 1995; 231 Mejstrik, Protasov (br0280) 2023; 4 Cicone (10.1016/j.laa.2025.06.024_br0070) 2010; 432 Moision (10.1016/j.laa.2025.06.024_br0100) 2001; 47 Rota (10.1016/j.laa.2025.06.024_br0310) 1960; 63 Hare (10.1016/j.laa.2025.06.024_br0220) 2011; 226 Guglielmi (10.1016/j.laa.2025.06.024_br0180) 2005; 27 Möller (10.1016/j.laa.2025.06.024_br0290) 2014; 463 Daubechies (10.1016/j.laa.2025.06.024_br0080) 1992; 23 Gurvits (10.1016/j.laa.2025.06.024_br0110) 1995; 231 Guglielmi (10.1016/j.laa.2025.06.024_br0320) Guglielmi (10.1016/j.laa.2025.06.024_br0200) 2008; 428 Guglielmi (10.1016/j.laa.2025.06.024_br0130) 2011; 49 Wright (10.1016/j.laa.2025.06.024_br0360) Blondel (10.1016/j.laa.2025.06.024_br0050) 2003; 24 Mejstrik (10.1016/j.laa.2025.06.024_br0260) 2020; 46 Berger (10.1016/j.laa.2025.06.024_br0060) 1992; 166 Jungers (10.1016/j.laa.2025.06.024_br0230) 2009 Mengi (10.1016/j.laa.2025.06.024_br0240) 2006 Mengi (10.1016/j.laa.2025.06.024_br0340) Trefethen (10.1016/j.laa.2025.06.024_br0090) 2005 Möller (10.1016/j.laa.2025.06.024_br0270) 2015 Guglielmi (10.1016/j.laa.2025.06.024_br0150) 2013; 13 Blondel (10.1016/j.laa.2025.06.024_br0030) 2013; 64 Guglielmi (10.1016/j.laa.2025.06.024_br0140) 2001; 32 Mejstrik (10.1016/j.laa.2025.06.024_br0280) 2023; 4 Hendrickx (10.1016/j.laa.2025.06.024_br0330) 2011 Guglielmi (10.1016/j.laa.2025.06.024_br0160) 2016; 37 Lagarias (10.1016/j.laa.2025.06.024_br0250) 1995; 214 Guglielmi (10.1016/j.laa.2025.06.024_br0210) 2009; 31 Parrilo (10.1016/j.laa.2025.06.024_br0300) 2008; 428 Protasov (10.1016/j.laa.2025.06.024_br0120) 2000; 191 Ahmadi (10.1016/j.laa.2025.06.024_br0010) 2011; 52 Guglielmi (10.1016/j.laa.2025.06.024_br0170) 2024; 93 Bousch (10.1016/j.laa.2025.06.024_br0040) 2002; 15 Guglielmi (10.1016/j.laa.2025.06.024_br0190) 2007; 14 Barabanov (10.1016/j.laa.2025.06.024_br0020) 1988; 49 Mejstrik (10.1016/j.laa.2025.06.024_br0350) |
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| SubjectTerms | Exact computation Finite tree algorithm Invariant polytope algorithm Joint spectral radius Pseudo spectral radius |
| Title | A hybrid approach to joint spectral radius computation |
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