IDEAS home Printed from https://ideas.repec.org/a/spr/cejnor/v27y2019i2d10.1007_s10100-018-0557-4.html
   My bibliography  Save this article

Numerical analysis of parallel implementation of the reorthogonalized ABS methods

Author

Listed:
  • Szabina Fodor

    (Corvinus University of Budapest)

  • Zoltán Németh

    (Corvinus University of Budapest)

Abstract

Solving systems of equations is a critical step in various computational tasks. We recently published a novel ABS-based reorthogonalization algorithm to compute the QR factorization. Experimental analysis on the Matlab 2015a platform revealed that this new ABS-based algorithm was able to more accurately calculate the rank of the coefficient matrix, the determination of the orthogonal bases and the QR factorization than the built-in rank or qr Matlab functions. However, the reorthogonalization process significantly increased the computation cost. Therefore, we tested a new approach to accelerate this algorithm by implementing it on different parallel platforms. The above mentioned ABS-based reorthogonalization algorithm was implemented using Matlab’s parallel computing toolbox and accelerated massive parallelism (AMP) runtime library. We have tested various matrices including Pascal, Vandermonde and randomly generated dense matrices. The performance of the parallel algorithm was determined by calculating the speed-up factor defined as the fold reduction of execution time compared to the sequential algorithm. For comparison, we also tested the effect of parallel implementation of the classical Gram–Schmidt algorithm incorporating a reorthogonalization step. The results show that the achieved speed-up is significant, and also the performance of this practical parallel algorithm increases as the number of equations grows. The results reveal that the reorthogonalized ABS algorithm is practical and efficient. This fact expands the practical usefulness of our algorithms.

Suggested Citation

  • Szabina Fodor & Zoltán Németh, 2019. "Numerical analysis of parallel implementation of the reorthogonalized ABS methods," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(2), pages 437-454, June.
    • Handle: RePEc:spr:cejnor:v:27:y:2019:i:2:d:10.1007_s10100-018-0557-4
    DOI: 10.1007/s10100-018-0557-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10100-018-0557-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10100-018-0557-4?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. Szabina Fodor, 2001. "Symmetric and Non-Symmetric ABS Methods for Solving Diophantine Systems of Equations," Annals of Operations Research, Springer, vol. 103(1), pages 291-314, March.
    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. József Abaffy & Szabina Fodor, 2021. "ABS-Based Direct Method for Solving Complex Systems of Linear Equations," Mathematics, MDPI, vol. 9(19), pages 1-17, October.

    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. József Abaffy & Szabina Fodor, 2021. "ABS-Based Direct Method for Solving Complex Systems of Linear Equations," Mathematics, MDPI, vol. 9(19), pages 1-17, October.
    2. Spedicato Emilio & Bodon Elena & Xia Zunquan & Mahdavi-Amiri Nezam, 2010. "ABS methods for continuous and integer linear equations and optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(1), pages 73-95, March.

    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:spr:cejnor:v:27:y:2019:i:2:d:10.1007_s10100-018-0557-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.