东南大学学报（英文版）2006，Vol.22Issue(4)：445-450,6.
基于平衡同时Schur分解的联合特征值估计
Joint eigenvalue estimation by balanced simultaneous Schur decomposition
摘要
Abstract
The problem of joint eigenvalue estimation for the non-defective commuting set of matrices A is addressed. A procedure revealing the joint eigenstmcture by simultaneous diagonalization of A with simultaneous Schur decomposition (SSD) and balance procedure alternately is proposed for performance considerations and also for overcoming the convergence difficulties of previous methods based only on simultaneous Schur form and unitary transformations. It is shown that the SSD procedure can be well incorporated with the balancing algorithm in a pingpong manner, i. e., each optimizes a cost function and at the same time serves as an acceleration procedure for the other. Under mild assumptions, the convergence of the two cost functions alternately optimized, i. e., the norm of A and the norm of the left-lower part of A, is proved. Numerical experiments are conducted in a multi-dimensional harmonic retrieval application and suggest that the presented method converges considerably faster than the methods based on only unitary transformation for matrices which are not near to normality.关键词
波达方向估计/多维谐波提取/联合特征值/同时Schur分解/平衡算法Key words
direction of arrival/multi-dimensional harmonic retrieval/joint eigenvalue/simultaneous Schur decomposition/balance algorithm分类
信息技术与安全科学引用本文复制引用
付佗,高西奇..基于平衡同时Schur分解的联合特征值估计[J].东南大学学报（英文版）,2006,22(4):445-450,6.基金项目
The National Natural Science Foundation of China(No. 60572072, 60496311 ), the National High Technology Research and Development Program of China (863 Program ) (No.2003AA123310), the International Cooperation Project on Beyond 3G Mobile of China ( No. 2005DFA10360). （No. 60572072, 60496311 ）
