IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2019i1p2-d299255.html
   My bibliography  Save this article

Generalized Inverses Estimations by Means of Iterative Methods with Memory

Author

Listed:
  • Santiago Artidiello

    (Instituto Tecnológico de Santo Domingo (INTEC), 10602 Santo Domingo, Dominican Republic)

  • Alicia Cordero

    (Multidisciplinary Institute of Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Juan R. Torregrosa

    (Multidisciplinary Institute of Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • María P. Vassileva

    (Instituto Tecnológico de Santo Domingo (INTEC), 10602 Santo Domingo, Dominican Republic)

Abstract

A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A . For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the matrix is singular, an approximation of the Moore–Penrose inverse and Drazin inverse are obtained. The convergence and the order of convergence is presented in each case. Some numerical tests allowed us to confirm the theoretical results and to compare the performance of our method with other known ones. With these results, the iterative methods with memory appear for the first time for estimating the solution of a nonlinear matrix equations.

Suggested Citation

  • Santiago Artidiello & Alicia Cordero & Juan R. Torregrosa & María P. Vassileva, 2019. "Generalized Inverses Estimations by Means of Iterative Methods with Memory," Mathematics, MDPI, vol. 8(1), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:2-:d:299255
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/2/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/2/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Yihui Lei & Zhengqi Dai & Bolin Liao & Guangping Xia & Yongjun He, 2022. "Double Features Zeroing Neural Network Model for Solving the Pseudoninverse of a Complex-Valued Time-Varying Matrix," Mathematics, MDPI, vol. 10(12), pages 1-19, June.

    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:gam:jmathe:v:8:y:2019:i:1:p:2-:d:299255. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.