New Pivot Selection for Sparse Symmetric Indefinite Factorization

TL;DR

This paper introduces a new pivot selection method for sparse symmetric indefinite matrix factorization that improves sparsity and stability, outperforming existing methods like MA57.

Contribution

A novel pivot selection technique combining minimum degree algorithm with stability considerations for better sparse factorization.

Findings

Produces sparser factors than MA57

Maintains numerical stability

Enhances sparsity without sacrificing stability

Abstract

We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our method produces factors that are sparser than the factors computed by MA57 and are stable.