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Accelerated Randomized Coordinate Descent for Solving Linear Systems

Author

Listed:
  • Qin Wang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Weiguo Li

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Wendi Bao

    (College of Science, China University of Petroleum, Qingdao 266580, China)

  • Feiyu Zhang

    (College of Science, China University of Petroleum, Qingdao 266580, China)

Abstract

The randomized coordinate descent (RCD) method is a simple but powerful approach to solving inconsistent linear systems. In order to accelerate this approach, the Nesterov accelerated randomized coordinate descent method (NARCD) is proposed. The randomized coordinate descent with the momentum method (RCDm) is proposed by Nicolas Loizou, we will provide a new convergence boundary. The global convergence rates of the two methods are established in our paper. In addition, we show that the RCDm method has an accelerated convergence rate by choosing a proper momentum parameter. Finally, in numerical experiments, both the RCDm and the NARCD are faster than the RCD for uniformly distributed data. Moreover, the NARCD has a better acceleration effect than the RCDm and the Nesterov accelerated stochastic gradient descent method. When the linear correlation of matrix A is stronger, the NARCD acceleration is better.

Suggested Citation

  • Qin Wang & Weiguo Li & Wendi Bao & Feiyu Zhang, 2022. "Accelerated Randomized Coordinate Descent for Solving Linear Systems," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4379-:d:979023
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    References listed on IDEAS

    as
    1. NESTEROV, Yurii, 2012. "Efficiency of coordinate descent methods on huge-scale optimization problems," LIDAM Reprints CORE 2511, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Ion Necoara & Yurii Nesterov & François Glineur, 2017. "Random Block Coordinate Descent Methods for Linearly Constrained Optimization over Networks," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 227-254, April.
    3. 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.
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