{'fraction_non_alphanumeric': 0.02280130293159609, 'fraction_numerical': 0.0, 'mean_word_length': 5.932330827067669, '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}}
Iterative solution methods based on the Hierarchically Semi-Separable Representation

In this paper, we study an important class of structured matrices: ”Hierarchically Semi-Separable (HSS)” matrices, for which an efficient hierarchical state based representation called Hierarchically Semi-Separable (HSS) representation can be used to utilize the data sparsity of the HSS matrices. A novel algorithm with O(n) complexity is proposed to construct suboptimal HSS representations from sparse matrices. Subsequently, the limitation of the direct HSS solution method is discussed in this paper, and a general strategy to combine standard iterative solution methods with the HSS representation is presented. We also describe a number of preconditioner construction algorithms based on the HSS representation. Our numerical experiments indicate that these iterative solution methods have linear complexity in computation time.