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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. Fast multipole method - Wikipedia

    en.wikipedia.org/wiki/Fast_multipole_method

    The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem.It does this by expanding the system Green's function using a multipole expansion, which allows one to group sources that lie close together and treat them as if they are a single source.

  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. 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

  7. Commutant lifting theorem - Wikipedia

    en.wikipedia.org/wiki/Commutant_lifting_theorem

    The commutant lifting theorem states that if is a contraction on a Hilbert space, is its minimal unitary dilation acting on some Hilbert space (which can be shown to exist by Sz.-Nagy's dilation theorem), and is an operator on commuting with , then there is an operator on commuting with such that

  8. 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.

  9. 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.