{'fraction_non_alphanumeric': 0.01904761904761905, 'fraction_numerical': 0.0, 'mean_word_length': 5.63063063063063, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the regularizing properties of a full multigrid method for ill-posed problems

For the stable solution of a linear ill-posed operator equation 𝒯x = 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.