数学
奇异值分解
奇异值
应用数学
反向
规范(哲学)
趋同(经济学)
收敛速度
背景(考古学)
基质(化学分析)
迭代法
系数矩阵
数学优化
算法
特征向量
钥匙(锁)
计算机科学
几何学
物理
生物
古生物学
量子力学
复合材料
经济
计算机安全
材料科学
法学
政治学
经济增长
出处
期刊:Inverse Problems
[IOP Publishing]
日期:2021-08-27
卷期号:37 (10): 105004-105004
被引量:4
标识
DOI:10.1088/1361-6420/ac1778
摘要
For solving the large-scale linear systems, a unified randomized row iterative (RRI) method was proposed in Gower and Richtarik (SIAM J. Matrix Anal. Appl., 36: 1660-1690, 2015), where its mean squared error is shown to decrease exponentially under some induced energy norm. In this work, for solving the perturbed system of linear equations, we give a new convergence analysis for the RRI method in the context of inverse problems. We divide the total error into two parts: the low- and high- frequency errors, which fully exploits the weighted singular value decomposition of the coefficient matrix. The upper bounds in the convergence rate of these two errors of RRI are analyzed for a noisy right-hand side, which can be specialized to the noise-free right-hand side case. Our estimates are compared with the upper bounds in Jiao, Jin and Lu (Inverse Problems, 33: 125012, 2017) when RRI is reduced to the standard randomized Kaczmarz method. Finally we present numerical examples to confirm the analysis.
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