Gauss-Newton methods with grid refinement
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.
Key words and phrasesGauß-Newton method parameter identification mesh independence
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