{'fraction_non_alphanumeric': 0.01699029126213592, 'fraction_numerical': 0.0048543689320388345, 'mean_word_length': 5.111111111111111, '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}}
A new variant of restarted GMRES

GMRES is an attractive iterative method for solving large non-symmetric algebraic linear systems. Computational and storage constraints usually force the method to be restarted after a fixed (small) number of iterations with subsequent loss of monotonic convergence properties. Trouble may be caused by the presence of eigenvalues close to the origin which are not well detected by early restarts. Unlike recent techniques that propose to include this information in later restarts, we use a new formulation of GMRES to derive a simple variant of the algorithm. The new approach attempts to mitigate stagnation by exploiting the smoothness of a certain polynomial near zero, resorting to the original method once convergence becomes truly monotonic. Copyright © 1999 John Wiley & Sons, Ltd.