阿诺迪迭代法
数学
特征向量
趋同(经济学)
里兹法
应用数学
通货紧缩
幂迭代
广义最小残差法
理论(学习稳定性)
块(置换群论)
Krylov子空间
迭代法
基质(化学分析)
还原(数学)
数学优化
数学分析
计算机科学
边值问题
几何学
货币政策
复合材料
经济
物理
机器学习
材料科学
货币经济学
量子力学
经济增长
作者
Richard B. Lehoucq,Danny C. Sorensen
标识
DOI:10.1137/s0895479895281484
摘要
A deflation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses, the Ritz value approximations of the eigenvalues converge at different rates. A numerically stable scheme is introduced that implicitly deflates the converged approximations from the iteration. We present two forms of implicit deflation. The first, a locking operation, decouples converged Ritz values and associated vectors from the active part of the iteration. The second, a purging operation, removes unwanted but converged Ritz pairs. Convergence of the iteration is improved and a reduction in computational effort is also achieved. The deflation strategies make it possible to compute multiple or clustered eigenvalues with a single vector restart method. A block method is not required. These schemes are analyzed with respect to numerical stability, and computational results are presented.
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