On Generalized Gaussian Quadratures for Exponentials and Their Applications

By Gregory Beylkin, Lucas Monzón. 2002

89 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/6d967347877b6b0b8a99d3f96f08671db6a9c836

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In Applied Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Approximation of bandlimited functions (2006, methodology): “Justification that the first method works can be found in [1], while a proof that the second method works can be found in [2].”
On approximation of functions by exponential sums (2005, methodology): “Even though most of the results in [11] are based on the particular properties of band functions, and as such, cannot be directly obtained by the general method of this paper, som in [11] are immediate consequences of the general approach presented here.”
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “Eﬃcient sum-of-exponentials approximation for the power function t − β ( β > 0 ) has been studied in detail both anaytically and algorithmically in a sequence of papers [5, 6, 7].”
Approximation by exponential sums revisited (2010, unknown): “We note that the special case of purely imaginary exponents ηm in (67) is treated in [15].”
Wavelets Based on Prolate Spheroidal Wave Functions (2004, methodology): “However, modern computational facilities and the recently developed numerical algorithms of Beylkin and Monzon [ 1 ] and of Xiao, Rokhlin and Yarvin [26] promise to provide elegant numerical results with satisfactory complexity.”
Algorithms for Numerical Analysis in High Dimensions (2005, methodology): “15) is addressed in [5] by extending methods in [4].”
Numerical construction of Green's functions in high dimensional elliptic problems with variable coefficients and analysis of renewable energy data via sparse and separable approximations (2012, background): “We begin by stating a key theoretical result developed in [19, 20].”