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Efficient Reduction Algorithms for Banded Symmetric Generalized Eigenproblems via Sequentially Semiseparable (SSS) Matrices

Author

Listed:
  • Fan Yuan

    (College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
    These authors contributed equally to this work.)

  • Shengguo Li

    (College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China
    These authors contributed equally to this work.)

  • Hao Jiang

    (College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China)

  • Hongxia Wang

    (College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China)

  • Cheng Chen

    (Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China)

  • Lei Du

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China)

  • Bo Yang

    (College of Computer Science and Technology, National University of Defense Technology, Changsha 410073, China)

Abstract

In this paper, a novel algorithm is proposed for reducing a banded symmetric generalized eigenvalue problem to a banded symmetric standard eigenvalue problem, based on the sequentially semiseparable (SSS) matrix techniques. It is the first time that the SSS matrix techniques are used in such eigenvalue problems. The newly proposed algorithm only requires linear storage cost and O ( n 2 ) computation cost for matrices with dimension n , and is also potentially good for parallelism. Some experiments have been performed by using Matlab, and the accuracy and stability of algorithm are verified.

Suggested Citation

  • Fan Yuan & Shengguo Li & Hao Jiang & Hongxia Wang & Cheng Chen & Lei Du & Bo Yang, 2022. "Efficient Reduction Algorithms for Banded Symmetric Generalized Eigenproblems via Sequentially Semiseparable (SSS) Matrices," Mathematics, MDPI, vol. 10(10), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1676-:d:815048
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