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arXiv · 2002.03400

Butterfly factorization via randomized matrix-vector multiplications

Yang Liu·Xin Xing·Han Guo·Eric Michielssen·Pieter Ghysels·Xiaoye Sherry Li
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Abstract

This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a $m\times n$ matrix with $m\approx n$ provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of $O(\log n)$ sparse factors, each containing $O(n)$ nonzero entries. The factorization can be attained using $O(n^{3/2}\log n)$ computation and $O(n\log n)$ memory resources. The proposed algorithm applies to matrices with strong and weak admissibility conditions arising from surface integral equation solvers with a rigorous error bound, and is implemented in parallel.

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Yang Liu, Xin Xing, Han Guo, Eric Michielssen, Pieter Ghysels, Xiaoye Sherry Li. 2020-02-09. Butterfly factorization via randomized matrix-vector multiplications. https://arxiv.org/abs/2002.03400

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