Fast multipole methods for approximating a function from sampling values

DOI10.1007/s11075-017-0279-zzbMath1421.65004OpenAlexW2586197211MaRDI QIDQ1681777

Guidong Liu, Shuhuang Xiang

Publication date: 24 November 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-017-0279-z

zbMATH Keywords

Lagrange interpolationfast multipole methodbarycentric interpolationarithmetic operationsrational barycentric interpolation

Mathematics Subject Classification ID

Numerical interpolation (65D05) Algorithms for approximation of functions (65D15) Discrete potential theory (31C20)

Related Items (4)

Barycentric prolate interpolation and pseudospectral differentiation ⋮ Superconvergence and fast implementation of the barycentric prolate differentiation ⋮ Fast computation of the spectral differentiation by the fast multipole method ⋮ On fast multipole methods for Fredholm integral equations of the second kind with singular and highly oscillatory kernels

Uses Software

• Chebfun
• RECFMM

Cites Work

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• Linear barycentric rational quadrature
• Convergence rates of derivatives of a family of barycentric rational interpolants
• Error bounds for approximation in Chebyshev points
• Rational functions for guaranteed and experimentally well-conditioned global interpolation
• Chebfun and numerical quadrature
• Statistical application of barycentric rational interpolants: an alternative to splines
• Barycentric rational interpolation with no poles and high rates of approximation
• Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix
• Explicit barycentric weights for polynomial interpolation in the roots or extrema of classical orthogonal polynomials
• Die Lage der Nullstellen eines Polynoms. IV
• THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX
• An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
• A Fast Adaptive Multipole Algorithm for Particle Simulations
• Exponential convergence of a linear rational interpolant between transformed Chebyshev points
• An Improved Fast Multipole Algorithm for Potential Fields on the Line
• Barycentric Lagrange Interpolation
• The numerical stability of barycentric Lagrange interpolation
• Fast Algorithms for Polynomial Interpolation, Integration, and Differentiation
• Computing Zeros on a Real Interval through Chebyshev Expansion and Polynomial Rootfinding
• <scp>REC</scp>FMM: Recursive Parallelization of the Adaptive Fast Multipole Method for Coulomb and Screened Coulomb Interactions
• On the convergence rates of Legendre approximation
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Implementing Clenshaw-Curtis quadrature, I methodology and experience
• Lagrangian Interpolation at the Chebyshev Points xn,     cos (  /n),   = 0(1)n; some Unnoted Advantages
• On Interpolation Approximation: Convergence Rates for Polynomial Interpolation for Functions of Limited Regularity
• Method of Lagrangian curvilinear interpolation
• A fast algorithm for particle simulations

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