Sparse Approximate Multifrontal Factorization with Butterfly Compression for High Frequency Wave Equations

An efficient multi-core implementation of a novel HSS-structured multifrontal solver using randomized sampling

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factorization leads to a solver with lower computational complexity than the standard multifrontal method fo…

Butterfly factorization via randomized matrix-vector multiplications

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 e…

串行稀疏Cholesky分解算法中可使用的一些新技术

Some new techniques to use in serial sparse Cholesky factorization algorithms

本文提出两种串行右视超节点稀疏Cholesky分解新变体，通过超节点内列重排序减少并增大非对角块，其中RLB无需浮点工作存储且不执行组装，在使用多线程BLAS时显著快于现有方法。