A Novel Greedy Block Gauss-Seidel Method for Solving Large Linear Least-Squares Problems

被引：0

作者：

Sun, Chao ^{[1
]}

Guo, Xiao-Xia ^{[1
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China

来源：

COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION | 2024年

基金：

中国国家自然科学基金;

关键词：

Greedy strategy; Linear least-squares problem; Block Gauss-Seidel method; Convergence property; COORDINATE DESCENT METHOD; TOMOGRAPHY;

D O I：

10.1007/s42967-024-00417-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a new convergence upper bound for the greedy Gauss-Seidel (GGS) method proposed by Zhang and Li [38]. The new convergence upper bound improves the upper bound of the GGS method. In addition, we also propose a novel greedy block Gauss-Seidel (RDBGS) method based on the greedy strategy of the GGS method for solving large linear least-squares problems. It is proved that the RDBGS method converges to the unique solution of the linear least-squares problem. Numerical experiments demonstrate that the RDBGS method has superior performance in terms of iteration steps and computation time.

引用

页数：18

共 38 条

[21]

Jin LL, 2022, Arxiv, DOI arXiv:2203.02153

[22] Randomized Methods for Linear Constraints: Convergence Rates and Conditioning [J].

Leventhal, D. ;

Lewis, A. S. .

MATHEMATICS OF OPERATIONS RESEARCH, 2010, 35 (03) :641-654

[23]

Li HY, 2020, Arxiv, DOI arXiv:2004.02476

[24] AN ACCELERATED RANDOMIZED PROXIMAL COORDINATE GRADIENT METHOD AND ITS APPLICATION TO REGULARIZED EMPIRICAL RISK MINIMIZATION [J].

Lin, Qihang ;

Lu, Zhaosong ;

Xiao, Lin .

SIAM JOURNAL ON OPTIMIZATION, 2015, 25 (04) :2244-2273

[25] On maximum residual block and two-step Gauss-Seidel algorithms for linear least-squares problems [J].

Liu, Yong ;

Jiang, Xiang-Long ;

Gu, Chuan-Qing .

CALCOLO, 2021, 58 (02)

[26] CONVERGENCE PROPERTIES OF THE RANDOMIZED EXTENDED GAUSS-SEIDEL AND KACZMARZ METHODS [J].

Ma, Anna ;

Needell, Deanna ;

Ramdas, Aaditya .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2015, 36 (04) :1590-1604

[27] A new randomized Gauss-Seidel method for solving linear least-squares problems [J].

Niu, Yu-qi ;

Zheng, Bing .

APPLIED MATHEMATICS LETTERS, 2021, 116

[28]

Nutini J, 2016, arXiv

[29]

Quarteroni A., 2002, Numerical Mathematics

[30]

RUHE A, 1983, LINEAR ALGEBRA APPL, V52-3, P591

← 1 2 3 4 →