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  2. Polynomial regression - Wikipedia

    en.wikipedia.org/wiki/Polynomial_regression

    Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. [1]

  3. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define this more precisely, the maximum number of inflection points possible in a polynomial curve is n-2, where n is the order of the polynomial equation. An inflection point is a location on the curve where it switches from a positive radius to ...

  4. Polynomial and rational function modeling - Wikipedia

    en.wikipedia.org/wiki/Polynomial_and_rational...

    For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. The rational function model is a generalization of the polynomial model: rational function models contain polynomial models as a subset (i.e., the case when the denominator is a constant).

  5. Characteristic equation (calculus) - Wikipedia

    en.wikipedia.org/wiki/Characteristic_equation...

    Characteristic equation (calculus) ... Therefore, the general case for u(x) is a polynomial of degree k − 1, so that u(x) = c 1 + c 2 x + c 3 x 2 + ⋯ + c k x k ...

  6. Horner's method - Wikipedia

    en.wikipedia.org/wiki/Horner's_method

    In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation.Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. [1]

  7. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    Polynomial interpolation also forms the basis for algorithms in numerical quadrature (Simpson's rule) and numerical ordinary differential equations (multigrid methods). In computer graphics, polynomials can be used to approximate complicated plane curves given a few specified points, for example the shapes of letters in typography.

  8. Approximation theory - Wikipedia

    en.wikipedia.org/wiki/Approximation_theory

    Calculating the derivatives of a polynomial is straightforward. One must also be able to calculate the first and second derivatives of f(x). Remez's algorithm requires an ability to calculate (), ′ (), and ″ to extremely high precision. The entire algorithm must be carried out to higher precision than the desired precision of the result.

  9. Collocation method - Wikipedia

    en.wikipedia.org/wiki/Collocation_method

    In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...

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