Hierarchical Orthogonal Factorization: Sparse Square matrices

@article{Gnanasekaran2022HierarchicalOF,
  title={Hierarchical Orthogonal Factorization: Sparse Square matrices},
  author={Abeynaya Gnanasekaran and Eric F Darve},
  journal={ArXiv},
  year={2022},
  volume={abs/2010.06807}
}
In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsify the separators in a Nested Dissection based Householder QR factorization. First, a modified version of Nested Dissection is used to identify interiors/separators and reorder the matrix. Then, classical Householder QR is used to factorize the interiors, going from the leaves to the root to the elimination tree. After… 
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