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  2. Theory of functional connections - Wikipedia

    en.wikipedia.org/wiki/Theory_of_functional...

    The Theory of Functional Connections (TFC) is a mathematical framework designed for functional interpolation.It introduces a method to derive a functional— a function that operates on another function—capable of transforming constrained optimization problems into equivalent unconstrained problems.

  3. Interpolation - Wikipedia

    en.wikipedia.org/wiki/Interpolation

    The Theory of Functional Connections (TFC) is a mathematical framework specifically developed for functional interpolation.Given any interpolant that satisfies a set of constraints, TFC derives a functional that represents the entire family of interpolants satisfying those constraints, including those that are discontinuous or partially defined.

  4. Basis function - Wikipedia

    en.wikipedia.org/wiki/Basis_function

    In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).

  5. Radial basis function interpolation - Wikipedia

    en.wikipedia.org/wiki/Radial_basis_function...

    Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of radial basis functions .

  6. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    We fix the interpolation nodes x 0, ..., x n and an interval [a, b] containing all the interpolation nodes. The process of interpolation maps the function f to a polynomial p. This defines a mapping X from the space C([a, b]) of all continuous functions on [a, b] to itself.

  7. Multivariate interpolation - Wikipedia

    en.wikipedia.org/wiki/Multivariate_interpolation

    In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.

  8. Category:Theorems in functional analysis - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in...

    Closed graph theorem (functional analysis) Closed range theorem; Cohen–Hewitt factorization theorem; Commutant lifting theorem; Commutation theorem for traces; Continuous functional calculus; Convex series; Cotlar–Stein lemma

  9. Lagrange polynomial - Wikipedia

    en.wikipedia.org/wiki/Lagrange_polynomial

    Lagrange and other interpolation at equally spaced points, as in the example above, yield a polynomial oscillating above and below the true function. This behaviour tends to grow with the number of points, leading to a divergence known as Runge's phenomenon ; the problem may be eliminated by choosing interpolation points at Chebyshev nodes .