Abstract
We consider the Gauß-Newton method for the solution of nonlinear least squares problems in the context of parameter identification problems. A scheme is presented in which the discretization error is controlled in such a way that in the initial phase of the algorithm a rather coarse grid level is being used whereas a refinement takes place as one moves closer to the solution of the problem. The theoretical justification is a mesh independence result on the rate of convergence for the iterates produced by the Gauß-Newton method. If the refinement of the mesh is done at a linear or quadratic rate then the method with mesh refinement during the iteration retains the linear or quadratic rate of convergence.
Visiting the Department of Mathematical Sciences, Rice University, Houston, Texas 77251-1892. This research was partially supported by Gottlieb-Daimler-und Karl-Benz-Stiftung, Ladenburg and NSF, Cooperate of Agreement No. CCR-8809615
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Heinkenschloss, M., Laumen, M., Sachs, E.W. (1991). Gauss-Newton methods with grid refinement. In: Desch, W., Kappel, F., Kunisch, K. (eds) Estimation and Control of Distributed Parameter Systems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 100. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6418-3_11
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DOI: https://doi.org/10.1007/978-3-0348-6418-3_11
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