On accurate error estimates for the quaternion least squares and weighted least squares problems

被引：3

作者：

Li, Ying ^{[1
]}

Wei, Musheng ^{[1
,2
]}

Zhang, Fengxia ^{[1
]}

Zhao, Jianli ^{[1
]}

机构：

[1] Liaocheng Univ, Coll Math Sci, Liaocheng 252000, Shandong, Peoples R China

[2] Shanghai Normal Univ, Coll Math & Sci, Shanghai 200234, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2020年 / 97卷 / 08期

关键词：

Error estimate; effective condition number; quaternion matrix; least squares problem; weighted least squares problem; EFFECTIVE CONDITION NUMBER; PERTURBATION BOUNDS; PSEUDOINVERSE; ALGORITHMS;

D O I：

10.1080/00207160.2019.1642469

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study error estimates of the quaternion least squares problem and the quaternion weighted least squares problem. For different cases, we define different condition numbers and effective condition numbers. We propose upper bounds of absolute and relative errors of the minimal norm LS solution and the general LS solution of the quaternion least squares problem and the quaternion weighted least squares problem, respectively, by using different condition numbers and effective condition numbers to make error estimates sharper.

引用

页码：1662 / 1677

页数：16

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