Overview of total least-squares methods
Overview of total least-squares methods
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DOI：
10.1016/j.sigpro.2007.04.004
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发表时间：
2007-10-01
影响因子：
4.4
通讯作者：
Van Huffel, Sabine
中科院分区：
文献类型：
--
作者：
Markovsky, Ivan;Van Huffel, Sabine
我们回顾了经典总体最小二乘法的发展和扩展，并描述了将其推广到加权和结构化近似问题的算法。在一般情况下，经典总体最小二乘问题有唯一解，该解根据数据矩阵的奇异值分解以解析形式给出。加权和结构化总体最小二乘问题没有这样的解析解，目前通过局部优化方法进行数值求解。我们解释了如何利用权重矩阵和数据矩阵的特殊结构进行高效的代价函数和一阶导数计算。这使得能够获得计算高效的求解方法。总体最小二乘法系列在系统理论、信号处理和计算机代数中有广泛的应用。我们描述了其在反卷积、线性预测和含误差变量系统辨识中的应用。（c）2007爱思唯尔B.V. 版权所有。
We review the development and extensions of the classical total least-squares method and describe algorithms for its generalization to weighted and structured approximation problems. In the generic case, the classical total least-squares problem has a unique solution, which is given in analytic form in terms of the singular value decomposition of the data matrix. The weighted and structured total least-squares problems have no such analytic solution and are currently solved numerically by local optimization methods. We explain how special structure of the weight matrix and the data matrix can be exploited for efficient cost function and first derivative computation. This allows to obtain computationally efficient solution methods. The total least-squares family of methods has a wide range of applications in system theory, signal processing, and computer algebra. We describe the applications for deconvolution, linear prediction, and errors-in-variables system identification. (c) 2007 Elsevier B. V. All rights reserved.