Approximating the Gaussian as a Sum of Exponentials and Its Applications to the Fast Gauss Transform

DOI10.4208/cicp.OA-2021-0031zbMath1486.30107WikidataQ114021246 ScholiaQ114021246MaRDI QIDQ5065159

Shidong Jiang, Leslie F. Greengard

Publication date: 18 March 2022

Published in: Communications in Computational Physics (Search for Journal in Brave)

zbMATH Keywords

rational approximationfast Gauss transformapproximation of the Gaussian kernel

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Approximation by rational functions (41A20) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Complexity and performance of numerical algorithms (65Y20)

Related Items (1)

A kernel-independent sum-of-exponentials method

Uses Software

• Matlab

Cites Work

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• Rational Carathéodory-Fejér approximation on a disk, a circle, and an interval
• Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
• A sharp error estimate for the fast Gauss transform
• A new version of the fast Gauss transform
• On the numerical inversion of the Laplace transform of certain holomorphic mappings
• Approximation by exponential sums revisited
• Efficient sum-of-exponentials approximations for the heat kernel and their applications
• A bootstrap method for sum-of-poles approximations
• Talbot quadratures and rational approximations
• On approximation of functions by exponential sums
• An improved Talbot method for numerical Laplace transform inversion
• Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems
• Infinite Hankel matrices and generalized Caratheodory-Fejer and I. Schur problems
• The Exponentially Convergent Trapezoidal Rule
• The Fast Generalized Gauss Transform
• The Carathéodory–Fejér Method for Real Rational Approximation
• All optimal Hankel-norm approximations of linear multivariable systems and theirL,^∞-error bounds†
• Real VS. Complex Rational Chebyshev Approximation on an Interval
• The Fast Gauss Transform with Variable Scales
• Parabolic and hyperbolic contours for computing the Bromwich integral
• A Spectral Order Method for Inverting Sectorial Laplace Transforms
• EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS
• Real Polynomial Chebyshev Approximation by the Carathéodory–Fejér method
• The Accurate Numerical Inversion of Laplace Transforms
• The Anisotropic Truncated Kernel Method for Convolution with Free-Space Green's Functions
• An Adaptive Fast Gauss Transform in Two Dimensions
• Real and complex Chebyshev approximation on the unit disk and interval
• A New Error Estimate of the Fast Gauss Transform
• Improved contour integral methods for parabolic PDEs
• The Fast Gauss Transform

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