精化双正交Lanczos方法  

The Refined Biorthogonalization Lanczos Method

作　　者：王耀卫[1] 

机构地区：[1]仰恩大学数学系,福建泉州362014

出　　处：《四川师范大学学报（自然科学版）》2013年第6期866-870,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：福建省教育厅科技项目(JA12360)资助项目

摘　　要：根据精化投影方法的思想对经典的双正交Lanczos方法进行改进,提出了精化双正交Lanczos方法,即把非对称矩阵A的投影矩阵Tm构造成另一个三对角矩阵Tm,理论上T m与Tm具有相同的特征值,而且TTm=Tm,并用矩阵Tm的特征值作为A的特征值的近似,进一步用A的左、右精化向量分别近似矩阵A的左、右特征向量.在计算过程中,Tm的特征值很容易得到,而且由它可计算高精度近似特征值.理论表明这种方法在计算大规模非对称特征问题方面比双正交Lanczos方法更为优越.We propose the refined biorthogonalization Lanczos method for modifying the classical biorthogonalization Lanczos method according to the refined projected method.First,we transform the projected matrix Tm of unsymmetric matrix A to obtain a tridiagonal matrix （T）m with the same eigenvalues,and （T）m satisfies （T）Tm =（T）m.We use the eigenvalues of matrix （T）m as the approximate eigenvalues of matrix A.At the same time,the left and right refined vectors of matrix A are used as the approximate left and right eigenvectors of matrix A respectively.The eigenvalues of matrix （T）m are easily computed,and it can be used to compute high precision approximate eigenvalues.The theory shows that the method is superior to the biorthogonalization Lanczos method in computing large unsymmetric eigen problems.

关 键 词：双正交Lanczos过程 RITZ值 Ritz向量 精化双正交Lanczos算法 

分 类 号：O241.6[理学—计算数学]