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Everything about Radial basis function
Type of mathematical function
In mathematics a radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, either the origin, so that, or some other fixed point, called a center, so that. Any function that satisfies the property is a radial function. The distance is usually Euclidean distance, although other metrics are sometimes used. They are often used as a collection which forms a basis for some function space of interest, hence the name. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Radial basis functionA 5-minute orientation
- Skim a recent paper: A Three-Level Radial Basis Function Method for Expensive OptimizationInfluential work since 2022
- Pick up a classic book: A primer on radial basis functions with applications to the geosciencesThe most-reprinted book on the subject
- Read the landmark paper: Universal Approximation Using Radial-Basis-Function NetworksCited 3,556 times
- Go sideways: Polyharmonic splineA closely related topic
- Go sideways: Kansa methodA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Universal Approximation Using Radial-Basis-Function Networks
Approximation and Radial-Basis-Function Networks
Radial basis function approximations: comparison and applications
Robust radial basis function neural networks
Median radial basis function neural network
Normalized Gaussian Radial Basis Function networks
Integrated multiquadric radial basis function approximation methods
Generalized multiscale radial basis function networks
🆕 Influential since 2022
A Three-Level Radial Basis Function Method for Expensive Optimization
A review of radial basis function with applications explored
Learning in Deep Radial Basis Function Networks
Mixed Radial Basis Function Neural Network Training Using Genetic Algorithm
Fuzzy Nonlinear Regression Modeling With Radial Basis Function Networks
📚 Books worth reading
A primer on radial basis functions with applications to the geosciencesBengt Fornberg · 2015
RADIAL BASIS FUNCTIONSMARTIN D. BUHMANN- 📕Regional gravity field modelling with radial basis functionsTobias Wittwer · 2009
- 📕Regional gravity field modeling with radial basis functionsTobias Wittwer · 2009
Construction of Global Lyapunov Functions Using Radial Basis Functions (Lecture Notes in Mathematics, No. 1904)Peter Giesl · 2007
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Polyharmonic spline In applied mathematics, polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting…
- Kansa method The Kansa method (also known as the unsymmetric radial basis function collocation method) is a meshless numerical method for solving partial differential…
- Geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction…
- Radial basis function interpolation Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured…
- Green's function for the three-variable Laplace equation In physics, the Green's function (or fundamental solution) for the Laplacian (or Laplace operator) in three variables is used to describe the response…
- Discontinuous Galerkin method In applied mathematics, discontinuous Galerkin methods (DG methods) form a class of numerical methods for solving differential equations. They combine…
- Positive-definite kernel In operator theory, a branch of mathematics, a positive-definite kernel is a generalization of a positive-definite function or a positive-definite matrix…
- Kolmogorov–Arnold Networks Kolmogorov–Arnold Networks (KANs) are a type of artificial neural network architecture inspired by the Kolmogorov–Arnold representation theorem, also known…