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  2. SciPy - Wikipedia

    en.wikipedia.org/wiki/SciPy

    SciPy (pronounced / ˈ s aɪ p aɪ / "sigh pie" [2]) is a free and open-source Python library used for scientific computing and technical computing. [3]SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering.

  3. Gaussian quadrature - Wikipedia

    en.wikipedia.org/wiki/Gaussian_quadrature

    The Gaussian quadrature chooses more suitable points instead, so even a linear function approximates the function better (the black dashed line). As the integrand is the polynomial of degree 3 ( y ( x ) = 7 x 3 – 8 x 2 – 3 x + 3 ), the 2-point Gaussian quadrature rule even returns an exact result.

  4. Generalized hypergeometric function - Wikipedia

    en.wikipedia.org/wiki/Generalized_hypergeometric...

    Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials.

  5. Gauss–Laguerre quadrature - Wikipedia

    en.wikipedia.org/wiki/Gauss–Laguerre_quadrature

    "Table of zeros and Gaussian Weights of certain Associated Laguerre Polynomials and the related Hermite Polynomials". Mathematics of Computation. 18 (88): 598– 616. doi: 10.1090/S0025-5718-1964-0166397-1. JSTOR 2002946. MR 0166397. Ehrich, S. (2002). "On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas".

  6. Gauss–Hermite quadrature - Wikipedia

    en.wikipedia.org/wiki/Gauss–Hermite_quadrature

    Weights versus x i for four choices of n. In numerical analysis, Gauss–Hermite quadrature is a form of Gaussian quadrature for approximating the value of integrals of the following kind:

  7. 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 .

  8. Gaussian function - Wikipedia

    en.wikipedia.org/wiki/Gaussian_function

    Mathematically, the derivatives of the Gaussian function can be represented using Hermite functions. For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale. Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory.

  9. Bayesian optimization - Wikipedia

    en.wikipedia.org/wiki/Bayesian_optimization

    Bayesian optimization of a function (black) with Gaussian processes (purple). Three acquisition functions (blue) are shown at the bottom. [8]Bayesian optimization is typically used on problems of the form (), where is a set of points, , which rely upon less (or equal to) than 20 dimensions (,), and whose membership can easily be evaluated.