雅可比矩阵与行列式
算法
非线性最小二乘法
数学
非线性系统
Levenberg-Marquardt算法
最小二乘函数近似
基质(化学分析)
可分离空间
计算机科学
应用数学
估计理论
人工智能
量子力学
人工神经网络
统计
物理
数学分析
复合材料
估计员
材料科学
作者
Min Gan,C. L. Philip Chen,Guangyong Chen,Long Chen
出处
期刊:IEEE transactions on cybernetics
[Institute of Electrical and Electronics Engineers]
日期:2018-10-01
卷期号:48 (10): 2866-2874
被引量:156
标识
DOI:10.1109/tcyb.2017.2751558
摘要
For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.
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