Accelerated Randomized Coordinate Descent for Solving Linear Systems

Qin Wang, Weiguo Li (), Wendi Bao and Feiyu Zhang
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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

Mathematics, 2022, vol. 10, issue 22, 1-20

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.

Keywords: Nesterov-accelerated; momentum; Kaczmarz method; large linear system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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