On condition numbers of quaternion matrix inverse and quaternion linear systems with multiple right-hand sides

IF 0.7 4区 数学 Q2 Mathematics
Qiaohua Liu, Shan Wang, Fengxia Zhang
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引用次数: 0

Abstract

This paper is devoted to the condition numbers of quaternion linear system with multiple right-hand sides and the associated condition numbers of the quaternion matrix inverse as well. The explicit expressions of the unstructured and structured normwise, mixed, and componentwise condition numbers for the system are given. To reduce the computational cost of the condition numbers,compact and tight upper bounds for these condition numbers are proposed. For general sparse and badly scaled problems, numerical examples show that mixed and componentwise condition numbers are preferred than the normwise condition number for estimating the forward error of the solution, and structured condition numbers are tighter than the unstructured ones for some specific structured problems.
四元数矩阵逆和多右手边四元数线性系统的条件数
本文研究了具有多右手边的四元数线性系统的条件数以及四元数矩阵逆的相关条件数。给出了系统的非结构化和结构化正态、混合和组件化条件数的显式表达式。为了减少条件数的计算量,提出了条件数的紧致上界。对于一般的稀疏和严重尺度问题,数值算例表明,混合和组件条件数比正态条件数更适合估计解的前向误差,并且对于某些特定的结构化问题,结构化条件数比非结构化条件数更严格。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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