Radial basis function approximation methods with extended precision floating point arithmetic

DOI10.1016/j.enganabound.2010.05.011zbMath1259.65173OpenAlexW2091355226MaRDI QIDQ1944430

Scott A. Sarra

Publication date: 25 March 2013

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2010.05.011

zbMATH Keywords

RBF interpolationextended precision floating point arithmeticRBF collocation for PDEs

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical interpolation (65D05)

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Uses Software

• Matlab
• XBLAS

Cites Work

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• Interpolation of scattered data: distance matrices and conditionally positive definite functions
• Eigenvalue stability of radial basis function discretizations for time-dependent problems
• Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
• Stable computation of multiquadric interpolants for all values of the shape parameter
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• On unsymmetric collocation by radial basis functions
• Error estimates and condition numbers for radial basis function interpolation
• Error estimate, optimal shape factor, and high precision computation of multiquadric collocation method
• Numerical Computing with IEEE Floating Point Arithmetic
• Stable Computations with Gaussian Radial Basis Functions
• A Stable Algorithm for Flat Radial Basis Functions on a Sphere
• Scattered Data Interpolation: Tests of Some Method
• Radial Basis Functions
• A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
• Design, implementation and testing of extended and mixed precision BLAS
• Scattered Data Approximation

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