Butterfly factorization via randomized matrix-vector multiplications
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This paper presents an adaptive randomized algorithm for computing the butterfly factorization of a m× n matrix with m≈ 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^3/2log n) computation and O(nlog 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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