On spectral and numerical properties of random butterfly matrices. (September 2019)

• Record Type: Journal Article
• Authors: Trogdon, Thomas
• Is Part Of: Applied mathematics letters. Volume 95(2019)
• Page Start: 48
• Page End: 58
• Publication Date: 2019-09
• Subjects: Butterfly matrices -- Fast matrix multiplication -- Random matrices; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2019.03.024
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.