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On some separated algorithms for separable nonlinear least squares problems
Gan M.2; Chen C.L.P.1; Chen G.-Y.2; Chen L.1
2018-10-01
Source PublicationIEEE Transactions on Cybernetics
ISSN21682267
Volume48Issue:10Pages:2866-2874
AbstractFor 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.
KeywordData fitting Jacobian approximation parameter estimation separable nonlinear least squares problems variable projection (VP)
DOI10.1109/TCYB.2017.2751558
URLView the original
Language英語
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Cited Times [WOS]:58   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Universidade de Macau
2.Fuzhou University
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GB/T 7714
Gan M.,Chen C.L.P.,Chen G.-Y.,et al. On some separated algorithms for separable nonlinear least squares problems[J]. IEEE Transactions on Cybernetics,2018,48(10):2866-2874.
APA Gan M.,Chen C.L.P.,Chen G.-Y.,&Chen L..(2018).On some separated algorithms for separable nonlinear least squares problems.IEEE Transactions on Cybernetics,48(10),2866-2874.
MLA Gan M.,et al."On some separated algorithms for separable nonlinear least squares problems".IEEE Transactions on Cybernetics 48.10(2018):2866-2874.
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