# Efficient Scalable Algorithms for Solving Dense Linear Systems with Hierarchically Semiseparable Structures

@article{Wang2013EfficientSA, title={Efficient Scalable Algorithms for Solving Dense Linear Systems with Hierarchically Semiseparable Structures}, author={Shen Wang and Xiaoye S. Li and Jianlin Xia and Yingchong Situ and Maarten V. de Hoop}, journal={SIAM J. Sci. Comput.}, year={2013}, volume={35} }

Hierarchically semiseparable (HSS) matrix techniques are emerging in constructing superfast direct solvers for both dense and sparse linear systems. Here, we develop a set of novel parallel algorithms for key HSS operations that are used for solving large linear systems. These are parallel rank-revealing QR factorization, HSS constructions with hierarchical compression, ULV HSS factorization, and HSS solutions. The HSS tree-based parallelism is fully exploited at the coarse level. The…

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