On approximation of functions by exponential sums

By Gregory Beylkin, Lucas Monzón. 2005

347 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis, Signal Processing

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Citations in the corpus

A literature survey of low‐rank tensor approximation techniques (2013, neutral): “For this purpose, various approaches have been discussed in [28–30, 37, 38].”
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].”
Counterparty Risk and Funding: A Tale of Two Puzzles (2014, methodology): “Instead, we use an approximate procedure based on exponential approximation of the so called hockey stick function, as presented in Iscoe, Jackson, Kreinin, and Ma (2010, 2013) based on Beylkin and Monzon (2005). We now briefly outline how to use this method for computing the price of a CDO tranche ”
Fractional viscoelastic models for power-law materials. (2020, background): “For this reason, power-law rheology can only be approximated by the spring-dashpot models that yield exponential terms with discrete time-scales [82–84].”
Adaptive Cross Approximation of Multivariate Functions (2011, methodology): “The method is based on the Adaptive Cross Approximation (ACA) initially designed for the approximation of bivariate functions.”
Mathematik in den Naturwissenschaften Leipzig Tensor-Product Approximation to Operators and Functions in High Dimensions (2007, methodology): “, based on Sinc-quadrature methods or an approximation by exponential sums (see case-study examples in [12, 3, 18]).”
Approximation by exponential sums revisited (2010, positive): “In [16] we use the Euler–Maclaurin formula to estimate the number of terms in the discretization of (2) as a function of the accuracy and the range of r.”