STRUCTURED TOTAL LEAST-SQUARES AND L2 APPROXIMATION-PROBLEMS
STRUCTURED TOTAL LEAST-SQUARES AND L2 APPROXIMATION-PROBLEMS
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DOI：
10.1016/0024-3795(93)90468-4
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发表时间：
1993-07-15
影响因子：
1.1
通讯作者：
DEMOOR, B
中科院分区：
文献类型：
--
作者：
DEMOOR, B
它显示了结构和加权的总最小二乘和L2近似问题如何导致“非线性”广义奇异值分解。提出了一种求（局部）最小值的逆迭代算法。本文的重点不在于算法的收敛性分析；相反，目的是说明其在系统和控制中的众多应用，包括具有相对误差和/或固定元素的总最小二乘法，逆奇异值问题，卡尔曼滤波器的变量误差变体，从噪声数据中实现脉冲响应，H-2模型简化，H-2系统识别，以及计算不确定线性系统的最大稳定半径。给出了几个数值算例。
It is shown how structured and weighted total least squares and L2 approximation problems lead to a ''nonlinear'' generalized singular value decomposition. An inverse iteration scheme to find a (local) minimum is proposed. The emphasis of the paper is not on the convergence analysis of the algorithm; rather the purpose is to illustrate its use in numerous applications in systems and control, including total least squares with relative errors and/or fixed elements, inverse singular value problems, an errors-in-variables variant of the Kalman filter, impulse response realization from noisy data, H-2 model reduction, H-2 system identification, and calculating the largest stability radius of uncertain linear systems. Several numerical examples are given.