Acta Numerica · 2006 · 279 citations · 158 references
ComputingComputer ScienceMathematicsComputational MechanicsFinite Element MethodsMachine LearningFinite Element DiscretizationKernel MethodsNumerical AlgorithmsNumerical AnalysisNumerical Methods For Differential EquationsPartial Differential EquationsConvolutional Neural NetworksKernel ApproximationKernel LearningNonlinear Partial Differential Equations
Kernels are valuable tools in various fields of numerical analysis, including approximation, interpolation, meshless methods for solving partial differential equations, neural networks, and machine learning. This contribution explains why and how kernels are applied in these disciplines. It uncovers the links between them, in so far as they are related to kernel techniques. It addresses non-expert readers and focuses on practical guidelines for using kernels in applications.
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N. Aronszajn · Transactions of the American Mathematical Society · 1950 · 5.4K citations · Full text
A two-dimensional interpolation function for irregularly-spaced data
Donald S. Shepard · 1968 · 5K citations
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