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Regularization Total Least Squares and Randomized Algorithms

Author

Listed:
  • Zhanshan Yang

    (School of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China)

  • Xilan Liu

    (School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721000, China)

  • Tiexiang Li

    (School of Mathematics, Southeast University, Nanjing 210096, China)

Abstract

In order to achieve an effective approximation solution for solving discrete ill-conditioned problems, Golub, Hansen, and O’Leary used Tikhonov regularization and the total least squares (TRTLS) method, where the bidiagonal technique is considered to deal with computational aspects. In this paper, the generalized singular value decomposition (GSVD) technique is used for computational aspects, and then Tikhonov regularized total least squares based on the generalized singular value decomposition (GTRTLS) algorithm is proposed, whose time complexity is better than TRTLS. For medium- and large-scale problems, the randomized GSVD method is adopted to establish the randomized GTRTLS (RGTRTLS) algorithm, which reduced the storage requirement, and accelerated the convergence speed of the GTRTLS algorithm.

Suggested Citation

  • Zhanshan Yang & Xilan Liu & Tiexiang Li, 2024. "Regularization Total Least Squares and Randomized Algorithms," Mathematics, MDPI, vol. 12(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1927-:d:1419695
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