M
Michael O'Neil
Researcher at New York University
Publications - 49
Citations - 1450
Michael O'Neil is an academic researcher from New York University. The author has contributed to research in topics: Integral equation & Quadrature (mathematics). The author has an hindex of 14, co-authored 47 publications receiving 1167 citations. Previous affiliations of Michael O'Neil include Yale University & Cornell University.
Papers
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Fast Direct Methods for Gaussian Processes
TL;DR: In this paper, the authors show that for the most commonly used covariance functions, the matrix $C$ can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an $\mathcal {O} (n\,\log^2, n)$ algorithm for inversion.
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Quadrature by expansion
TL;DR: This paper presents a systematic, high-order approach that works for any singularity (including hypersingular kernels), based only on the assumption that the field induced by the integral operator is locally smooth when restricted to either the interior or the exterior.
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An algorithm for the rapid evaluation of special function transforms
TL;DR: A new class of fast algorithms for the application to arbitrary vectors of certain special function transforms, including the Fourier–Bessel transform, the non-equispaced Fourier transform, transforms associated with all classical orthogonal polynomials, etc.
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Fast Direct Methods for Gaussian Processes
TL;DR: In this paper, the authors show that for the most commonly used covariance functions, the matrix $C$ can be hierarchically factored into a product of block low-rank updates of the identity matrix, yielding an $\mathcal O (n\log^2 n) $ algorithm for inversion.
Journal ArticleDOI
Fast algorithms for Quadrature by Expansion I: Globally valid expansions
TL;DR: In this paper, a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions is presented.