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Stable Evaluation of Gaussian Radial Basis Function Interpolants
SIAM Journal on Scientific Computing, 2012We provide a new way to compute and evaluate Gaussian radial basis function interpolants in a stable way with a special focus on small values of the shape parameter, i.e., for “flat” kernels. This work is motivated by the fundamental ideas proposed earlier by Bengt Fornberg and his coworkers.
Gregory E. Fasshauer, Michael J. McCourt
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Multivariate cardinal interpolation with radial-basis functions
Constructive Approximation, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Parallel Multivariate Interpolation Algorithm With Radial Basis Functions
International Journal of Computer Mathematics, 2003This paper presents an efficient and highly scalable parallel version of the Modified RBF Shepard's method presented in [5]. This method maintains the "metric" nature and the advantages of Shepard's method and, at the same time, improves its accuracy by exploiting the characteristics of flexibility and accuracy which have made the radial basis ...
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Optical distortion correction using radial basis function interpolation
Frontiers in Optics 2012/Laser Science XXVIII, 2012Optical distortion is often not corrected in compact optical systems prompting the need for post-processing distortion correction. We propose a distortion correction algorithm using radial basis functions and demonstrate real-time distortion correction.
Aaron Bauer +5 more
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Asymptotic coefficients for Gaussian radial basis function interpolants
Applied Mathematics and Computation, 2010Radial basis functions (RBFs) are used in multidimensional interpolation on irregular or scattered data. The form of the approximation is \[ f(\vec{x})\approx \sum_{j=1}^{N} \lambda_j\varphi(\| \vec{x}-\vec{x}_j\|_2), \quad x\in\mathbb R^d \] \((d\geq1)\) for some function \(\varphi(r)\) and some set of \(N\) points \(\vec{x}_j\), which are called the `
Boyd, John P., Wang, Lei
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Radial Basis Function Interpolation for Freehand 3D Ultrasound
1999Freehand 3D ultrasound imaging produces a set of irregularly spaced B-scans, which are typically reconstructed on a regular grid for visualisation and data analysis. Most standard reconstruction algorithms are designed to minimise computational requirements and do not exploit the underlying shape of the data.We investigate whether approximation with ...
Robert Rohling +3 more
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Hermite interpolation with radial basis functions on spheres
Advances in Computational Mathematics, 1999The author shows how conditionally negative definite functions on spheres complex with strictly monotone functions can be used for Hermite interpolation. Some numerical results are also presented.
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An error analysis for radial basis function interpolation
Numerische Mathematik, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Radial Basis Function Interpolation for Computational Aeroacoustics
AIAA AVIATION 2020 FORUM, 2020Stefan Schoder +3 more
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Interpolation of GPS Orbit Coordinates Using Radial Basis Functions
2017The satellite positions computation for many topics related to the astronomy and the satellite geodesy has been crucial. Thisis also one of the core tasks of many GNSS positioning software. In this study, the interpolation methods used in determining the GPS satellite coordinates were researched and the identification of the best suitable method was ...
Doğanalp, Serkan, Çakır, Recep
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