On the regularizing properties of a full multigrid method for ill-posed problems

For the stable solution of a linear ill-posed operator equation x = y we project the equation onto finite-dimensional spaces and apply a full multigrid method (MGM) with the smoother proposed by King. After giving level-independent contraction factor estimates for the corresponding symmetric multigrid operators, we study the regularizing properties of the corresponding full MGM with an a priori chosen finest level, proving convergence, with optimal rates under respective sourcewise representation conditions. We show applicability of the method to a parameter identification problem from inverse groundwater filtration, and give numerical results.

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