| Jacobi-Davidson方法中的修正方程和对应的精化方法 |
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| 引用本文： | 贾仲孝,冯绍强. Jacobi-Davidson方法中的修正方程和对应的精化方法[J]. 数学研究及应用, 2005, 25(3): 515-524 |
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| 作者姓名： | 贾仲孝 冯绍强 |
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| 作者单位： | 1. 清华大学数学科学系,北京,100084
2. 大连理工大学应用数学系,辽宁,大连,116024 |
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| 基金项目： | 国家自然科学基金(10471074)国家重点基础研究规划项目(G1999032805)高等学校骨干教师基金． |
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| 摘 要： | Jacobi-Davidson方法的核心之一是求解用以合理扩展投影子空间的线性修正方程组,众多文献均认为该方程是自然有解的.本文详细研究了修正方程,证明它可能无解,并给出了解存在的条件.同时,为克服近似特征向量的可能不收敛性,提出了精化的Jacobi-Davidson方法,建立了对应的修正方程.
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| 关 键 词： | Jacobi-Davidson方法 精化的Jacobi-Davidson方法 Ritz值 Ritz向量 精化向量 修正方程 Rayleigh商 |
| 文章编号： | 1000-341X(2005)03-0515-10 |
| 收稿时间： | 2003-03-17 |
| 修稿时间： | 2003-03-17 |
A Refined Jacobi-Davidson Method and Its Correction Equation |
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| JIA Zhong-xiao and FENG Shao-qiang. A Refined Jacobi-Davidson Method and Its Correction Equation[J]. Journal of Mathematical Research with Applications, 2005, 25(3): 515-524 |
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| Authors: | JIA Zhong-xiao and FENG Shao-qiang |
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| Affiliation: | Dept. of Math.; Tsinghua University; Beijing; China;Dept. of Appl. Math.; Dalian University of Technology; Liaoning; China |
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| Abstract: | A central problem in the Jacobi-Davidson method is to expand a projection subspace by solving certain correction equation. It has been commonly accepted that the correction equation always has a solution. However, it is proved in this paper that this is not true. Conditions are given to decide when it has a unqiue solution or many solutions or no solution. A refined Jacobi-Davidson method is proposed to overcome the possible nonconvergence of Ritz vectors by computing certain refined approximation eigenvectors from the subspace. A corresponding correction equation is derived for the refined method. |
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| Keywords: | Jacobi-Davidson method refined Jacobi-Davidson method Ritz value Ritz vector refined eigenvector approximation correction equation Rayleigh quotient. |
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