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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.
In order to overcome the defects of convergence and performance analysis based on simultaneous Schur decomposition and unitary transformation, a joint feature estimation algorithm based on simultaneous similar diagonalization is proposed. The algorithm The diagonalization of the matrix family is achieved by alternating Schur decompositions and norm balancing for A. The effectiveness of this algorithm is that each subprocess accelerates the convergence of another subprocess while optimizing its own cost function Under appropriate assumptions, the convergence of the two cost functions (matrix family norm and triangular family norm under the family of families), which are alternately optimized, can be proved.The numerical simulation based on multi-dimension harmonic extraction The convergence rate of the matrix family deviating from the regular matrix is significantly faster than that based on the simultaneous Schur decomposition and the unitary transform algorithm, and the joint eigenvalue estimation performance can be succinctly closed analysis.