摘要
The refined Arnoldi method proposed by Jia is used for computing some eigen-pairs of large matrices. In contrast to the Arnoldi method, the fundamental dif-ference is that the refined method seeks certain refined Ritz vectors, which aredifferent from the Ritz vectors obtained by the Arnoldi method, from a projection space with minimal residuals to approximate the desired eigenvectors. In com-parison with the Ritz vectors, the refined Ritz vectors are guaranteed to converge theoretically and can converge much faster numerically. In this paper we propose to replace the Ritz values, obtained by the Arnoldi method with respect to a Krylovsubspace, by the ones obtained with respect to the subspace spanned by the refined Ritz vectors. We discuss how to compute these new approximations cheaply and reliably. Theoretical error bounds between the original Ritz values and the new Ritz values are established. Finally, we present a variant of the refined Arnoldi al-gorithm for an augmented Krylov subspace and discuss restarting issue. Numerical results confirm efficiency of the new algorithm.
The refined Arnoldi method proposed by Jia is used for computing some eigen-pairs of large matrices. In contrast to the Arnoldi method, the fundamental difference is that the refined method seeks certain refined Ritz vectors, which are different from the Ritz vectors obtained by the Arnoldi method, from a projection space with minimal residuals to approximate the desired eigenvectors. In comparison with the Ritz vectors, the refined Ritz vectors are guaranteed to converge theoretically and can converge much faster numerically. In this paper we propose to replace the Ritz values, obtained by the Arnoldi method with respect to a Krylov subspace, by the ones obtained with respect to the subspace spanned by the refined Ritz vectors. We discuss how to compute these new approximations cheaply and reliably. Theoretical error bounds between the original Ritz values and the new Ritz values are established. Finally, we present a variant of the refined Arnoldi algorithm for an augmented Krylov subspace and discuss restarting issue. Numerical results confirm efficiency of the new algorithm.
出处
《数值计算与计算机应用》
CSCD
北大核心
2003年第2期101-110,共10页
Journal on Numerical Methods and Computer Applications
基金
国家重点基础研究发展规划项目(973)(G1999032805)
高等学校骨干教师基金资助
