RANK-DEFICIENT NONLINEAR LEAST SQUARES PROBLEMS AND SUBSET SELECTION

We examine the local convergence of the Levenberg—Marquardt method for the solution of nonlinear least squares problems that are rank-deficient and have nonzero residual. We show that replacing the Jacobian by a truncated singular value decomposition can be numerically unstable. We recommend instead...

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Vydáno v:SIAM journal on numerical analysis Ročník 49; číslo 3/4; s. 1244 - 1266
Hlavní autoři: IPSEN, I. C. F., KELLEY, C. T., POPE, S. R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Témata:
Algorithms
Approximation
Cauchy problem
Convergence
Decomposition
Exact sciences and technology
Jacobians
Least squares
Least squares method
Mathematical models
Mathematical vectors
Mathematics
Matrices
Nonlinear equations
Nonlinearity
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Parametric models
Perturbation methods
Sciences and techniques of general use
Studies
Zero
subset selection
65L09
Least squares problem
Nonlinear problems
Algorithm
15A18
nonlinear least squares
Numerical analysis
Least squares method
65F22
65F20
65F15
65K10
65H10
65F35
Abstract space
Levenberg-Marquardt algorithm
Singular value decomposition
ISSN:0036-1429, 1095-7170
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Shrnutí:We examine the local convergence of the Levenberg—Marquardt method for the solution of nonlinear least squares problems that are rank-deficient and have nonzero residual. We show that replacing the Jacobian by a truncated singular value decomposition can be numerically unstable. We recommend instead the use of subset selection. We corroborate our recommendations by perturbation analyses and numerical experiments.
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ISSN:0036-1429
1095-7170
DOI:10.1137/090780882