一组特征矩阵联合对角化算法的收敛性分析  

On global convergence of jointly approximate diagonalization algorithm for a set of eigenmatrices

作　　者：张海琴[1] 于力[1] 

机构地区：[1]西安电子科技大学理学院,陕西西安710071

出　　处：《西安电子科技大学学报》2002年第6期786-790,共5页Journal of Xidian University

基　　金：国家自然科学基金资助项目(69972037)

摘　　要：先将一组特征矩阵联合对角化问题转化为一种代价函数的优化问题,再利用梯度下降方法求解代价函数的最优点.研究了一类代价函数的一些基本性质和各种等价形式,分析了一组特征矩阵联合对角化算法的收敛性.分析结果表明一组特征矩阵联合对角化算法是一种不动点算法;在特征矩阵无误差情况下,这个算法单步迭代就收敛到理论解.The jointly approximate diagonalization for a set of eigenmatrices is a classical key problem in the matrix theory, signal processing and wireless communications. Generally, we first find a cost function of the jointly approximate diagonalization for a set of eigenmatrices such that an optimal solution of the cost function is associated with jointly approximate diagonalization for a set of eigenmatrices, and then obtain the solution of the jointly approximate diagonalization for a set of eigenmatrices by solving an optimal solution of the cost function. This paper studies some properties of the known cost function, gives its several equivalent forms and analyzes the global convergence of the jointly approximate diagonalization algorithm (JADA) for a set of eigenmatrices. Analysis results show that JADA is a fixedpoint algorithm ; when there is no error in a set of eigenmatrices, JADA converges to a global minimum point only in one step iteration; when there is an error in a set of eigenmatrices, JADA, at least, converges to a local minimum point.

关 键 词：收敛性 特征矩阵 联合对角化 双正交性 代价函数 信号处理 

分 类 号：TN911.7[电子电信—通信与信息系统]