非对称实矩阵特征问题的广义Lanczos方法的收敛性  

On Convergence of Generalized Lanczos Method for Unsymmetric Real Matrices

作　　者：贾仲孝[1] 熊西文[1] 

机构地区：[1]大连理工大学应用数学系

出　　处：《大连理工大学学报》1990年第1期1-7,共7页Journal of Dalian University of Technology

摘　　要：对大型非对称矩阵Ａ的特征问题，Ｓａａｄ曾证明，当Ａ只有实单重特征值时．广义Ｌａｎｃｚｏｓ方法对求Ａ 的端部特征值和对应的特征向量通常是快速收敛的。本文取消了对 Ａ的这一限制，在 Ａ只有线性初等因子的情形下，证明了广义 Ｌａｎｃ－ｚｏｓ方法对计算Ａ的少数端部特征值和对应的特征的量仍是快速收敛的。For eigenproblems of large unsymmetric real matrices, Saad has proved that if A has only real and simple eigenvalues,the generalized Lanczos method usually coverges rapidly for computing the outer eigenvalues and the corre- sponding eigenvectors of A. This paper drops this restriction to A,and shows that the generalized Lanczos method still converges rapidly for so1ving a few outer eigenvalues and the corresponding eigenvectors of A when A has only linear elementary divisors. Meanwhile, the authors point out the intrinsic drawback of the method.

关 键 词：非对称实矩阵 特征值 LANCZOS方法 

分 类 号：O241.6[理学—计算数学]