TITLE:
A Count Sketch Maximal Weighted Residual Kaczmarz Method with Oblique Projection for Highly Overdetermined Linear Systems
AUTHORS:
Peng Zhang, Longyan Li, Pingping Zhang
KEYWORDS:
Count Sketch, Oblique Projection, Kaczmarz Method, Linear System
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.12 No.4,
April
11,
2022
ABSTRACT: Motivated by the count sketch maximal weighted residual Kaczmarz (CS-MWRK) method presented by Zhang and Li (Appl. Math. Comput., 410, 126486), we combine the count sketch tech with the maximal weighted residual Kaczmarz Method with Oblique Projection (MWRKO) constructed by Wang, Li, Bao and Liu (arXiv: 2106.13606) to develop a new method for solving highly overdetermined linear systems. The convergence rate of the new method is analyzed. Numerical results demonstrate that our method performs better in computing time compared with the CS-MWRK and MWRKO methods.