用简单反迭代法计算三对角矩阵的特征向量  

COMPUTING EIGENVECTOR OF SYMMETRIC TRIDIAGONAL MATRIX BY USING SIMPLE INVERSE ITERATION

作　　者：欧阳添伟 张振跃[2] 

机构地区：[1]北京市161信箱，北京100036 [2]浙江大学数学系，杭州310027

出　　处：《高等学校计算数学学报》2002年第3期236-243,共8页Numerical Mathematics A Journal of Chinese Universities

摘　　要：The goal of this paper is to compute the eigenvector of symmetrictridiagonal matrix T corresponding to the given approximate eigenvalue λ, by us-ing one step of inverse iteration for certain chosen right vector ek. Careful analysis shows that for suitable chosen k, say kmax, the simple inverse iteration, onestep of inverse iteration, can give a high accurate eigenvector, and its accuracy isachieved for the approximate eigenvalue λ too. Some sufficient conditions of thatkd＝kmax are given. We also give an estimate to show that kd still works very welleven in the case when the sufficient conditions are not exactly satisfied.The goal of this paper is to compute the eigenvector of symmetric tridiagonal matrix T corresponding to the given approximate eigenvalue λ, by using one step of inverse iteration for certain chosen right vector ek. Careful analysis shows that for suitable chosen k, say kmax, the simple inverse iteration, one step of inverse iteration, can give a high accurate eigenvector, and its accuracy is achieved for the approximate eigenvalue λtoo. Some sufficient conditions of that kd=kmax are given. We also give an estimate to show that kd still works very well even in the case when the sufficient conditions are not exactly satisfied.

关 键 词：反迭代法 三对角矩阵 特征向量 

分 类 号：O241.6[理学—计算数学]