广义最小残量法研究与应用近况综述
An Overview of Recent Developments and Applications of the GMRES Method

作者: 马晓飞 :太原科技大学应用科学学院;

关键词: GMRES历史发展实际应用GMRES Historical Development Practical Application

摘要:
用于求解大型非对称线性方程组的广义最小残量法(GMRES)以其迭代速度快的优点广泛应用于科学工程计算。本文就GMRES算法的研究近况,分别对其历史发展和实际应用进行概括性的介绍。先从纵向概括了该算法的起源,并介绍了该算法发展过程中有突出影响的变形算法以及近期发展情况,再从横向阐述了近年内它在各领域的应用、与各领域之间的联系和对各领域产生的影响。最后对GMRES算法的进一步发展及应用作出展望。

Abstract:
The generalized minimum residual method (GMRES) is widely applied in the scientific and engi- neering computations due to its general merit of fast convergence. This paper presents a summary introduc- tion of the GMRES method for its historical development and practical applications, with an emphasis on its recent status. We start with a summary on the origin of the method, followed by some notable variants, to- gether with some recent developments. Then, we introduce some recent applications of the GMRES method in various research fields, pointing out its connection to and impact on these fields. Finally, we provide an outlook on the further development and applications of the GMRES method.

文章引用: 马晓飞 (2013) 广义最小残量法研究与应用近况综述。 理论数学, 3, 181-187. doi: 10.12677/PM.2013.33027

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