Rank-Deficient Nonlinear Least Squares Problems and Subset Selection

Authors:
I. C. F. Ipsen;C. T. Kelley;S. R. Pope
Affiliations:
ipsen@ncsu.edu and Tim_Kelley@ncsu.edu;-;scott.pope@gmail.com
Venue:
SIAM Journal on Numerical Analysis
Year:
2011

Citing 6
Cited 1

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Abstract

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.