# Questions tagged [rbf]

Radial Basis Functions (RBFs) are commonly used for interpolating scattered data, in numerical meshfree simulation methods, and in artificial neural networks

26 questions
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### Solution of ill conditioned RBF kernel to be used in Quadratic programming

This problem is similar to the one described here: Large-and-ill-conditioned-quadratic-convex-problem RBF kernel: Equation Reason for RBF being ill-conditioned: The kernel matrix K is singular when ...
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### How interpolate a huge cloud of scattered 3D points?

I have a cloud consist of a million scattered 3d points. I want to get a uniform cloud of 3d points. I think to interpolate in blocks. However, as shown in the figure grid, there is a problem of ...
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### RBF kernel mapping

I was reading that the Gaussian/RBF kernel maps its input onto the surface of normalized hypersphere. Our RBF kernel given by: $k(x,z) = exp(\frac{- ||x-z||^2}{2\sigma^2})$ Can anyone explain why ...
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### General Dimension of The RBF Interpolation

I am reading about the RBF interpolation in order to apply it to interpolate a bunch of data over a three dimensional space. This may sound as a simple question but it is annoying me not knowing it. ...
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### How to find the particular solution for Augmented Thin Plate Splines in the context of the Dual Reciprocity Boundary Element Method

In the dual reciprocity boundary element method (DRBEM) the non-homogeneous terms are expanded in terms of radial basis functions. This expansion involves approximating the solution to the linear ...
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### Matrix operations for RBF solver

GOAL: I got from someone the python code for an RBF solver. The solver stores 9 transformation matrix (each of which, once decomposed, have tx, ty and tz set at 0 and sx, sy and sz set to 1, so only ...
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### How does one approximate a second derivative with ATPS interpolation

When using the Dual Reciprocity Boundary Element Method ( or any radial basis function method ) to solve a nonlinear differential equation it is necessary to approximate some derivatives of a ...
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I have this question and I need help; What is the effect of using a more hidden layer on the performance of approximation of the RBF network?
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### How can I use RBF interpolation on a highly stretched rectangular domain?

I performed a 2D parametric analysis where one variable is much larger than the other. Basically I sampled a function in many points: let's say 5 points for $x_1$ and 5 points for $x_2$, where the ...
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### Confusion between Wendland RBF functions - missing Wendland functions

I need to compute Wendland functions for a project, and got confused between the formula to construct Wendland functions $\phi(d,k)$ where d is the dimension So in the original paper introducing ...
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### Radial Basis Fn vs. Wavelets (not Neural Networks)

I am interested in parameterizing a surface without a mesh. One technique used in the field of optics is to use Radial Basis Functions (e.g. Gaussians). From a naive point of view, the decomposition ...
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### Interpolation with RBF

I have a function that is continuous and differentiable over $\mathbb{R}$ and its support is the whole real line. I want to approximate it through a linear combination of Gaussian functions. I know ...