# State-of-The-Art Sparse Direct Solvers

arXiv: https://arxiv.org/abs/1907.05309 · HTML: https://mlsanity.com/paper/1907.05309/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [ReFill: Reinforcement Learning for Fill-In Minimization](https://mlsanity.com/paper/2501.16130/) (2025)

## Abstract (arXiv)

In this chapter we will give an insight into modern sparse elimination methods. These are driven by a preprocessing phase based on combinatorial algorithms which improve diagonal dominance, reduce fill-in, and improve concurrency to allow for parallel treatment. Moreover, these methods detect dense submatrices which can be handled by dense matrix kernels based on multithreaded level-3 BLAS. We will demonstrate for problems arising from circuit simulation, how the improvements in recent years have advanced direct solution methods significantly.