Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of radial basis functions.[1][2] RBF interpolation is a mesh-free method, meaning the nodes (points in the domain) need not lie on a structured grid, and does not require the formation of a mesh. It is often spectrally accurate[3] and stable for large numbers of nodes even in high dimensions.
Many interpolation methods can be used as the theoretical foundation of algorithms for approximating linear operators, and RBF interpolation is no exception. RBF interpolation has been used to approximate differential operators, integral operators, and surface differential operators.
^Hardy, Rolland (March 1971). "Multiquadric equations of topography and other irregular surfaces". Journal of Geophysical Research. 76 (8): 1905–1915. Bibcode:1971JGR....76.1905H. doi:10.1029/JB076i008p01905.
^Richard, Franke (January 1982). "Scattered Data Interpolation: Tests of Some Methods". Mathematics of Computation. 38 (157): 181–200. doi:10.1090/S0025-5718-1982-0637296-4.
^Buhmann, Martin; Nira, Dyn (June 1993). "Spectral convergence of multiquadric interpolation". Proceedings of the Edinburgh Mathematical Society. 36 (2): 319–333. doi:10.1017/S0013091500018411.
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In mathematics a radialbasisfunction (RBF) is a real-valued function φ {\textstyle \varphi } whose value depends only on the distance between the input...
Radialbasisfunction (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured...
theory, basisfunctions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basisfunctions provides...
mathematical modeling, a radialbasisfunction network is an artificial neural network that uses radialbasisfunctions as activation functions. The output of the...
(cSSIM) has been introduced and studied in the context of Radialbasisfunctioninterpolation. SSIMULACRA and SSIMULACRA2 are variants of SSIM developed...
two-dimensional window function is shared by its two-dimensional Fourier transform. The difference between the separable and radial forms is akin to the...
splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." They...
likely to be treated as K separate scalar-output basisfunctions). An example of this is radialbasisfunctions (RBF's), which compute some transformed version...
determines its interpolation error. There exist a number of mathematical theories concerning the family of multiquadric radialbasisfunctions and providing...
energy-minimizing spline interpolation. Surrogates.jl is a Julia packages which offers tools like random forests, radialbasis methods and kriging. Linear...
polynomial basis-functions are used along with new basisfunctions, such as splines, radialbasisfunctions, and wavelets. These families of basisfunctions offer...
graphics, a hierarchical RBF is an interpolation method based on Radialbasisfunctions (RBF). Hierarchical RBF interpolation has applications in the construction...
Smoothed point interpolation method (S-PIM) (2005). Meshfree local radial point interpolation method (RPIM). Local radialbasisfunction collocation Method...
"tuning", so automatic interpolation is feasible. This is not the case for other radialbasisfunctions. For example, the Gaussian function e − k ⋅ r 2 {\displaystyle...
tools for handling and solving small dense linear systems. RadialBasisFunctioninterpolation and parametrization even with large set of nodes. Sorting...
Bessel function of the first kind with order n + 2k − 2/2. When k = 0 this gives a useful formula for the Fourier transform of a radialfunction. This...
modeling Artificial neural networks including Multilayer perceptrons Radialbasisfunction networks Support vector machines Due to the limited number of training...
of polynomial and radialbasisfunctions in the creation of shape functions (it accommodates the discontinuous displacement functions, as long as it is...
gap applications. Also the signal quality is much higher, enabling [interpolation] within the sensor/encoder or by an external circuit. There is a limit...
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