On spectral and numerical properties of random butterfly matrices
On spectral and numerical properties of random butterfly matrices
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DOI：
10.1016/j.aml.2019.03.024
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发表时间：
2017-09
期刊：
影响因子：
--
通讯作者：
T. Trogdon
中科院分区：
文献类型：
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作者：
T. Trogdon
讨论了帕克（1995）提出的随机正交蝴蝶矩阵类的谱和数值性质，包括特征值分布的均匀性。这些矩阵很重要，因为矩阵向量与N维向量的乘积可以在O（N log N）操作中执行。在最简单的情况下，这些随机矩阵与正交群的子群上的Haar测度一致。我们讨论的背景下，随机线性代数的其他影响。
Spectral and numerical properties of classes of random orthogonal butterfly matrices, as introduced by Parker (1995), are discussed, including the uniformity of eigenvalue distributions. These matrices are important because the matrix–vector product with an N-dimensional vector can be performed in O (N log N) operations. In the simplest situation, these random matrices coincide with Haar measure on a subgroup of the orthogonal group. We discuss other implications in the context of randomized linear algebra.