IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v300y2017icp1-20.html
   My bibliography  Save this article

Recurrent neural network for computing the W-weighted Drazin inverse

Author

Listed:
  • Wang, Xue-Zhong
  • Ma, Haifeng
  • Stanimirović, Predrag S.

Abstract

Two gradient based recurrent neural networks (RNNs) for computing the W-weighted Drazin inverse of a real rectangular matrix are proposed and considered. Usage of the first RNN is limited by a specific constraint on the spectrum of a certain matrix. The second RNN is usable without restrictions. The stability of the recurrent neural networks as well as their convergence are considered. Numerical examples are given to show the efficiency of the proposed neural networks.

Suggested Citation

  • Wang, Xue-Zhong & Ma, Haifeng & Stanimirović, Predrag S., 2017. "Recurrent neural network for computing the W-weighted Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 300(C), pages 1-20.
    • Handle: RePEc:eee:apmaco:v:300:y:2017:i:c:p:1-20
    DOI: 10.1016/j.amc.2016.11.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316307068
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.11.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hernández, A. & Lattanzi, M. & Thome, N., 2016. "On some new pre-orders defined by weighted Drazin inverses," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 108-116.
    2. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469.
    3. Kyrchei, Ivan, 2015. "Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 453-465.
    4. Yimin Wei & Hebing Wu, 2001. "Challenging Problems on the Perturbation of Drazin Inverse," Annals of Operations Research, Springer, vol. 103(1), pages 371-378, March.
    5. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    6. Xia, Youshen & Zhang, Songchuan & Stanimirović, Predrag S., 2016. "Neural network for computing pseudoinverses and outer inverses of complex-valued matrices," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 1107-1121.
    7. Hernández, A. & Lattanzi, M. & Thome, N., 2015. "Weighted binary relations involving the Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 215-223.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Khosro Sayevand & Ahmad Pourdarvish & José A. Tenreiro Machado & Raziye Erfanifar, 2021. "On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus," Mathematics, MDPI, vol. 9(19), pages 1-23, October.
    3. Ma, Haifeng & Stanimirović, Predrag S., 2019. "Characterizations, approximation and perturbations of the core-EP inverse," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 404-417.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Coll, C. & Lattanzi, M. & Thome, N., 2018. "Weighted G-Drazin inverses and a new pre-order on rectangular matrices," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 12-24.
    2. Håvard Hungnes, 2016. "Using common factors to identify substitution possibilities in a factor demand system with technological changes," Discussion Papers 849, Statistics Norway, Research Department.
    3. Caner, Mehmet & Fan, Qingliang, 2015. "Hybrid generalized empirical likelihood estimators: Instrument selection with adaptive lasso," Journal of Econometrics, Elsevier, vol. 187(1), pages 256-274.
    4. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    5. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    6. Juan Carlos Escanciano & Wei Li, 2013. "On the identification of structural linear functionals," CeMMAP working papers CWP48/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013. "Nelson–Plosser revisited: The ACF approach," Journal of Econometrics, Elsevier, vol. 175(1), pages 22-34.
    8. John H. J. Einmahl & Anna Kiriliouk & Andrea Krajina & Johan Segers, 2016. "An M-estimator of spatial tail dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 275-298, January.
    9. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    10. Pawel Janus & André Lucas & Anne Opschoor & Dick J.C. van Dijk, 2014. "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels," Tinbergen Institute Discussion Papers 14-073/IV, Tinbergen Institute, revised 19 Aug 2015.
    11. Abadir Karim M., 2012. "The Square Root of a Matrix," Journal of Time Series Econometrics, De Gruyter, vol. 4(2), pages 1-7, November.
    12. Rasmus Tangsgaard Varneskov, 2011. "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices," CREATES Research Papers 2011-35, Department of Economics and Business Economics, Aarhus University.
    13. Abadir Karim M. & Larsson Rolf, 2012. "Biases of Correlograms and of AR Representations of Stationary Series," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-11, May.
    14. Stanimirović, Predrag S. & Petković, Marko D. & Mosić, Dijana, 2022. "Exact solutions and convergence of gradient based dynamical systems for computing outer inverses," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    15. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    16. Drew Creal & Siem Jan Koopman & André Lucas, 2011. "A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 552-563, October.
    17. Harvey, Andrew & Thiele, Stephen, 2016. "Testing against changing correlation," Journal of Empirical Finance, Elsevier, vol. 38(PB), pages 575-589.
    18. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    19. Bertille Antoine & Eric Renault, 2017. "On the relevance of weaker instruments," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 928-945, October.
    20. Engwerda, J.C. & Weeren, A.J.T.M., 2006. "A Result on Output Feedback Linear Quadratic Control," Discussion Paper 2006-108, Tilburg University, Center for Economic Research.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:300:y:2017:i:c:p:1-20. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.