Multivariate Interpolation by Polynomials and Radial Basis Functions

By Robert Schaback. 2005

167 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/63a53387dcd21a24da4e7d508d10a20b0f6ebfc9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Natasha Flyer
2. Bengt Fornberg
3. Gregory E. Fasshauer
4. Jack G. Zhang
5. Robert Schaback
6. Victor Bayona
7. Gregory A. Barnett
8. Grady Barrett Wright

In Mechanics of Materials

1. Gregory E. Fasshauer
2. Natasha Flyer
3. Bengt Fornberg
4. A. J. Ferreira
5. Jack G. Zhang
6. Robert Schaback
7. Romesh C. Batra
8. Victor Bayona

In Statistical and Nonlinear Physics

1. Natasha Flyer
2. Bengt Fornberg
3. Gregory E. Fasshauer
4. Jack G. Zhang
5. Elisabeth Larsson
6. Gregory A. Barnett
7. Victor Bayona
8. Grady Barrett Wright

Citations in the corpus

• Stable Computations with Gaussian Radial Basis Functions (2011, methodology): “For Gaussian RBFs, the limit interpolant as the shape parameter ε → 0 exists for any distinct set of node points [9], [26].”
• On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy (2016, methodology): “When calculating in the small ε regime with a stable algorithm, it is not surprising that added polynomials offer no benefit, since the GA themselves virtually span the same function space and exactly the same space in the ε→ 0 limit [8, 21, 28].”
• The Runge phenomenon and spatially variable shape parameters in RBF interpolation (2007, background): “Results in [29] (page 308) can be shown to imply that the eigenvalues of the A-matrix will scale with different powers of ε.”
• Limit problems for interpolation by analytic radial basis functions (2008, methodology): “This interpolant was already studied in [15] and shown to be different from other polynomial interpolants like the one in [3].”
• On choosing “optimal” shape parameters for RBF approximation (2007, background): “, [1, 2, 28, 29]) that in the limiting case of “flat” basis functions, i.”
• Scattered node compact finite difference-type formulas generated from radial basis functions (2006, background): “Recently it has been shown [19] [20] [21] [22] that, under some mild restrictions on φ(r), the RBF interpolants converge to polynomial interpolants in the limit of φ(r) becoming entirely flat.”
• Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter (2008, background): “[43,44]) and Schaback [45] showed that certain limiting cases of radial basis functions correspond to polynomial interpolants.”