An Ulm-like algorithm for generalized inverse eigenvalue problems
In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math. 367 , 112485 2020 ) for the GIEP, we propose here an Ulm-like algori...
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| Vydáno v: | Numerical algorithms Ročník 98; číslo 3; s. 1611 - 1641 |
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| Abstract | In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math.
367
, 112485
2020
) for the GIEP, we propose here an Ulm-like algorithm for the GIEP. Compared with other existing methods for the GIEP, the proposed algorithm avoids solving the (approximate) Jacobian equations and so it seems more stable. Assuming that the relative generalized Jacobian matrices at a solution are nonsingular, we prove the quadratic convergence property of the proposed algorithm. Incidentally, we extend the work of Luo et al. (J. Nonlinear Convex Anal.
24
, 2309–2328
2023
) for the inverse eigenvalue problem (for short, IEP) to the GIEP. Some numerical examples are provided and comparisons with other algorithms are made. |
|---|---|
| AbstractList | In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math.
367
, 112485
2020
) for the GIEP, we propose here an Ulm-like algorithm for the GIEP. Compared with other existing methods for the GIEP, the proposed algorithm avoids solving the (approximate) Jacobian equations and so it seems more stable. Assuming that the relative generalized Jacobian matrices at a solution are nonsingular, we prove the quadratic convergence property of the proposed algorithm. Incidentally, we extend the work of Luo et al. (J. Nonlinear Convex Anal.
24
, 2309–2328
2023
) for the inverse eigenvalue problem (for short, IEP) to the GIEP. Some numerical examples are provided and comparisons with other algorithms are made. In this paper, we study the numerical solutions of the generalized inverse eigenvalue problem (for short, GIEP). Motivated by Ulm’s method for solving general nonlinear equations and the algorithm of Aishima (J. Comput. Appl. Math. 367, 112485 2020) for the GIEP, we propose here an Ulm-like algorithm for the GIEP. Compared with other existing methods for the GIEP, the proposed algorithm avoids solving the (approximate) Jacobian equations and so it seems more stable. Assuming that the relative generalized Jacobian matrices at a solution are nonsingular, we prove the quadratic convergence property of the proposed algorithm. Incidentally, we extend the work of Luo et al. (J. Nonlinear Convex Anal. 24, 2309–2328 2023) for the inverse eigenvalue problem (for short, IEP) to the GIEP. Some numerical examples are provided and comparisons with other algorithms are made. |
| Author | Shen, Weiping Luo, Yusong |
| Author_xml | – sequence: 1 givenname: Yusong surname: Luo fullname: Luo, Yusong organization: School of Mathematical Sciences, Zhejiang Normal University – sequence: 2 givenname: Weiping surname: Shen fullname: Shen, Weiping email: shenweiping@zjnu.cn organization: School of Mathematical Sciences, Zhejiang Normal University |
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| Cites_doi | 10.1137/140972494 10.2514/3.11928 10.1137/0724043 10.1016/j.jco.2007.04.003 10.1002/nla.2327 10.1007/978-94-009-2754-4 10.2514/3.11634 10.1088/0266-5611/31/8/085007 10.1016/j.laa.2018.03.022 10.1016/j.cam.2019.112485 10.1016/j.cam.2019.04.031 10.1137/S0036142901393814 10.1080/01630569808816829 10.1007/BF01437039 10.1080/03081087.2016.1250864 10.1016/0024-3795(93)90329-M 10.1007/s00211-008-0144-z 10.1016/j.laa.2019.10.004 10.1088/0266-5611/17/2/302 10.1088/0266-5611/20/5/022 10.1016/j.laa.2022.11.014 10.1016/0024-3795(90)90129-Z 10.1002/(SICI)1099-0887(199609)12:9<531::AID-CNM999>3.0.CO;2-S 10.1016/S0024-3795(99)00109-3 10.1080/00207160.2021.1913728 10.1016/j.laa.2017.05.019 10.1017/S0962492902000016 10.1016/j.laa.2021.03.025 10.1002/(SICI)1099-1506(199701/02)4:1<1::AID-NLA95>3.0.CO;2-D 10.1023/A:1023611931016 10.1002/mma.7025 10.1016/j.apnum.2010.11.001 |
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| Keywords | Quadratic convergence Newton’s method 65F15 Generalized inverse eigenvalue problem 65H17 Ulm’s method 15A18 15A29 |
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