# 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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## 3 Citations

Hierarchical Orthogonal Factorization: Sparse Least Squares Problems

- Computer ScienceJ. Sci. Comput.
- 2022

A fast hierarchical solver for solving large, sparse least squares problems by using low-rank approximations on the frontal matrices to sparsify the vertex separators at every level in the elimination tree and showing that the runtime of the algorithm scales as O(M logN) and uses O( M) memory to store the factorization.

STM-multifrontal QR: streaming task mapping multifrontal QR factorization empowered by GCN

- Computer ScienceSC
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A graph convolutional network (GCN) for adaptively selecting the optimal reordering algorithm is proposed in symbolic analysis and an optimized tasks stream parallel processing strategy is proposed and a more efficient computing task mapping framework for NUMA architecture is adopted.

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- 2020

This note proposes to use the hierarchical interpolative factorization as the preconditioning for the conjugate gradient iteration of the Crank-Nicholson time stepping method, and offers an efficient and accurate approximate inverse of the linear system.

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