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  2. Theory of functional connections - Wikipedia

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

    The consistency problem, which pertains to constraints, interpolation, and functional interpolation, is comprehensively addressed in. [3] This includes the consistency challenges associated with boundary conditions that involve shear and mixed derivatives. The univariate version of TFC can be expressed in one of the following two forms:

  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. Fixed-point iteration - Wikipedia

    en.wikipedia.org/wiki/Fixed-point_iteration

    The fixed point iteration x n+1 = cos x n with initial value x 1 = −1.. An attracting fixed point of a function f is a fixed point x fix of f with a neighborhood U of "close enough" points around x fix such that for any value of x in U, the fixed-point iteration sequence , (), (()), ((())), … is contained in U and converges to x fix.

  5. Category:Interpolation - Wikipedia

    en.wikipedia.org/wiki/Category:Interpolation

    This page was last edited on 28 January 2020, at 04:45 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  6. 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).

  7. Newton polynomial - Wikipedia

    en.wikipedia.org/wiki/Newton_polynomial

    Newton's formula is of interest because it is the straightforward and natural differences-version of Taylor's polynomial. Taylor's polynomial tells where a function will go, based on its y value, and its derivatives (its rate of change, and the rate of change of its rate of change, etc.) at one particular x value.

  8. 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.

  9. 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 .