High Quality Content by WIKIPEDIA articles! A radial basis function (RBF) is a real-valued function whose value depends only on the distance from the origin, so that phi(mathbf{x}) = phi(|mathbf{x}|); or alternatively on the distance from some other point c, called a center, so that phi(mathbf{x}, mathbf{c}) = phi(|mathbf{x}-mathbf{c}|). Any function ? that satisfies the property phi(mathbf{x}) = phi(|mathbf{x}|) is a radial function. The norm is usually Euclidean distance, although other distance functions are also possible. For example by using Lukaszyk-Karmowski metric it is for some radial functions possible to avoid problems with ill conditioning of the matrix solved to determine coefficients wi (see below), since the |mathbf{x}| is always greater than zero. Sums of radial basis functions are typically used to approximate given functions. This approximation process can also be interpreted as a simple kind of neural network.

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