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An inexact Levenberg-Marquardt method for large sparse nonlinear least squares. (English) Zbl 0562.65041

A method for solving the nonlinear least squares problem \(\min \| f(x)\|^ 2_ 2,\) \(f: {\mathbb{R}}^ n\to {\mathbb{R}}^ m\), is roughly sketched, which is intended especially to solve large problems with a sparse Jacobian J(x) of f(x). The method is quite similar to the well- known Levenberg-Marquardt method, however, in each step the linear system of equations defining the Levenberg-Marquardt correction is solved approximately by the iterative LSQR-method of C. C. Paige and M. A. Saunders [ACM Trans. Math. Software 8, 43-71 (1982; Zbl 0478.65016)]. Without proof some global and local convergence results are reported which seem rather satisfactory.
Reviewer: R.Hettich

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Citations:

Zbl 0478.65016
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