摘要
本文提出一些高收敛率的Ｒａｙｌｅｉｇｈ商型迭代格式，用以求解矩阵特征值问题ＡＸ＝λＸ，Ａ∈Ｃｎｘｎ。对于正规矩阵Ａ，本文的ｌ级ＨＲＱＩ法具有２ｌ＋１阶局部敛率。著名的ＲＱＩ法就是１级ＨＲＱＩ法。在时，如用Ｇａｕｓｓ消元法解有关的线性方程组，则ｌ级ＨＲＱＩ格式在每个迭代步中的计算量与ＲＱＩ的计算量基本持平。对非正规矩阵，与著名的Ｏｓｔｒｏｗｓｋｉ双边迭代法（ＯＴ）相对应，本文提出Ｉ级ＨＯＴＩ迭代格式。ｌ级ＨＯＴＩ用于非亏损矩阵时，具有２ｌ＋１阶局部效率。而ＯＴＩ就是１级ＨＯＴＩ法。同样，ｌ级ＨＯＴＩ与ＯＴＩ的每步迭代的计算量基本持平。
In the paper, some Rayleigh quotient iteration type schemes(RQI--type) for matrix eigenvalue problem Ax=λX, A∈C nxn(1) are proPOsed. They are HRQI and HOTI schemes. For normal matrix A, the l-th grad HRQI has local convergence rate ZI+l, where l is a given natural number. The well--known RQI [1] [2] is just the l-st grad HRQI. If the Gauss elemination method is used to solve relevallt linear systems and , then in each iteration step, the flop's order required by the l-th HRQI is about the same as one required by the RQI. For nonnormal matrix A, the case is similar to above between the well-known Ostrowski,s Two-Sided iteration(OTI) and the l-th grad HOTI.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
1996年第2期16-25,共10页
Journal of East China Normal University(Natural Science)
关键词
Rayleigh商迭代
高收敛率
双边迭代
矩阵
特征值
Rayleigh quotient iteration (RQI) HRQI HOTI convergence rate normal matrix nonnormal matrix
