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Radial basis function interpolation
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<p>Radial basis function (RBF) interpolation is an advanced method in <a href="/facts/Approximation_theory/87AaPXLp">approximation theory</a> for constructing <a href="/facts/Order_of_accuracy/DYPPter1">high-order</a> accurate <a href="/facts/Interpolation/8PyetX4f">interpolants</a> of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of <a href="/facts/Radial_basis_function/QnWM1mBN">radial basis functions</a>. RBF interpolation is a <a href="/facts/Meshfree_method/uUhEQD3K">mesh-free method</a>, meaning the nodes (points in the domain) need not lie on a structured grid, and does not require the formation of a <a href="/facts/Types_of_mesh/vl32mAA3">mesh</a>. It is often spectrally accurate and stable for large numbers of nodes even in high dimensions. </p><p>Many interpolation methods can be used as the theoretical foundation of algorithms for approximating <a href="/facts/Linear_operator/Q1PBKNVV">linear operators</a>, and RBF interpolation is no exception. RBF interpolation has been used to approximate <a href="/facts/Differential_operator/Nr15J0IE">differential operators</a>, integral operators, and <a href="/facts/Differential_geometry_of_surfaces/cslVnmd6">surface differential operators</a>. </p>