| 基于平衡同时Schur分解的联合特征值估计 |
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| 引用本文： | 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,2006,22(4):445-450. |
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| 作者姓名： | 付佗 高西奇 |
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| 作者单位： | 东南大学移动通信国家重点实验室 南京210096 |
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| 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. 2005DFAI0360）. |
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| 摘 要： | 讨论可交换单纯矩阵族A的联合特征值估计问题.为了克服基于同时Schur分解和酉变换算法的收敛和性能分析缺陷,提出了一种基于同时相似对角化的联合特征结构估计算法.该算法通过对A交替进行同时Schur分解和范数平衡来实现矩阵族的对角化.该算法的有效性在于:每个子过程在优化自身代价函数的同时,还对另一子过程的收敛起到加速作用.在适当的假设条件下,可以证明该算法交替优化的2个代价函数(矩阵族范数和矩阵族下三角元素范数)的收敛性.基于多维谐波提取的数值仿真显示该算法在矩阵族偏离正规阵时收敛速度显著快于基于同时Schur分解和酉变换算法,并且联合特征值的估计性能可以进行简洁的闭式分析.
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| 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 |
| 收稿时间： | 04 28 2006 12:00AM |
Joint eigenvalue estimation by balanced simultaneous Schur decomposition |
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| Fu Tuo,Gao Xiqi.Joint eigenvalue estimation by balanced simultaneous Schur decomposition[J].Journal of Southeast University(English Edition),2006,22(4):445-450. |
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| Authors: | Fu Tuo Gao Xiqi |
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| Institution: | National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China |
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| Abstract: | The problem of joint eigenvalue estimation for the non-defective commuting set of matrices A is addressed.A procedure revealing the joint eigenstructure 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. |
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| Keywords: | direction of arrival multi-dimensional harmonic retrieval joint eigenvalue simultaneous Schur decomposition balance algorithm |
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