Structure preserving quaternion full orthogonalization method with applications

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-01-28 DOI:10.1002/nla.2495

Tao Li, Qingwen Wang

引用次数: 3

Abstract

This article proposes a structure‐preserving quaternion full orthogonalization method (QFOM) for solving quaternion linear systems arising from color image restoration. The method is based on the quaternion Arnoldi procedure preserving the quaternion Hessenberg form. Combining with the preconditioning techniques, we further derive a variant of the QFOM for solving the linear systems, which can greatly improve the rate of convergence of QFOM. Numerical experiments on randomly generated data and color image restoration problems illustrate the effectiveness of the proposed algorithms in comparison with some existing methods.

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保结构四元数全正交化方法及其应用

本文提出了一种保结构的四元数全正交化方法（QFOM），用于求解彩色图像恢复中产生的四元线性系统。该方法基于保留四元数Hessenberg形式的四元数Arnoldi过程。结合预处理技术，我们进一步推导了求解线性系统的QFOM的一个变体，它可以大大提高QFOM的收敛速度。在随机生成数据和彩色图像恢复问题上的数值实验表明，与现有的一些方法相比，所提出的算法是有效的。

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

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.