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Splitting-based randomized iterative methods for solving indefinite least squares problem

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  • Zhang, Yanjun
  • Li, Hanyu

Abstract

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose a simple and effective splitting (SP) method according to its own structure, and prove that it converges for any initial value. Further, to avoid implementing some matrix multiplications and calculating the inverse of large matrix, and considering the acceleration and efficiency of the randomized strategy, we develop two randomized iterative methods on the basis of the SP method as well as the randomized Kaczmarz, Gauss-Seidel and coordinate descent methods, and describe their convergence properties. Numerical results show that our three methods all have quite decent performance in both computing time and iteration numbers compared with the latest iterative method of the ILS problem, and also demonstrate that the two randomized methods indeed yield significant acceleration in terms of computing time.

Suggested Citation

  • Zhang, Yanjun & Li, Hanyu, 2023. "Splitting-based randomized iterative methods for solving indefinite least squares problem," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    • Handle: RePEc:eee:apmaco:v:446:y:2023:i:c:s0096300323000619
    DOI: 10.1016/j.amc.2023.127892
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    References listed on IDEAS

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    1. D. Leventhal & A. S. Lewis, 2010. "Randomized Methods for Linear Constraints: Convergence Rates and Conditioning," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 641-654, August.
    2. Md Sarowar Morshed & Md Saiful Islam & Md. Noor-E-Alam, 2020. "Accelerated sampling Kaczmarz Motzkin algorithm for the linear feasibility problem," Journal of Global Optimization, Springer, vol. 77(2), pages 361-382, June.
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    Cited by:

    1. Du, Kui, 2024. "Regularized randomized iterative algorithms for factorized linear systems," Applied Mathematics and Computation, Elsevier, vol. 466(C).

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