Rank-Deficient Nonlinear Least Squares Problems and Subset Selection
2011
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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