Structure Preserving Quaternion Biconjugate Gradient Method

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-01-22 DOI:10.1137/23m1547299

Tao Li, Qing-Wen Wang

引用次数: 0

Abstract

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 1, Page 306-326, March 2024.
Abstract. This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.

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结构保留四元双共轭梯度法

SIAM 矩阵分析与应用期刊》，第 45 卷，第 1 期，第 306-326 页，2024 年 3 月。摘要本文研究了一种新颖的结构保留方法，用于求解彩色图像去模糊问题中产生的非赫米四元线性系统。从每次迭代都保留四元数三边形的四元数 Lanczos 双正交化过程出发，我们推导出求解线性系统的四元数双共轭梯度法，然后建立了所提算法的收敛性分析。最后，我们提供了一些数值示例来说明我们的方法与 QGMRES 相比的可行性和有效性，特别是在计算时间方面。

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

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.