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arXiv · 2609.20241

VAC: A Volume-sampling-based Elimination Rule for Approximate Cholesky Factorization

Yves Baumann·Rasmus Kyng·Gernot Zöcklein
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Abstract

We propose Volume Appproximate Cholesky (VAC), an alternative sampling rule for practical approximate Cholesky algorithms. Our rule samples a uniformly random spanning tree of the arising product clique to reduce the fill-in generated at each step. Sampling a random spanning tree preserves the edgewise marginals of the provably correct scheme of (Kyng \& Sachdeva 2016), while ensuring connectivity in the spirit of the practical rule proposed in (Gao, Kyng \& Spielman 2023). Our sampling method is simple, provably linear time and also admits a $O(\log n)$ depth parallel implementation.

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Yves Baumann, Rasmus Kyng, Gernot Zöcklein. 2026-07-27. VAC: A Volume-sampling-based Elimination Rule for Approximate Cholesky Factorization. https://arxiv.org/abs/2609.20241

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