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In numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. [ 1 ]
In mathematics, Neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician Eric Harold Neville in 1934. Given n + 1 points, there is a unique polynomial of degree ≤ n which goes through the given points. Neville's algorithm evaluates this polynomial.
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
A solver based on polynomial interpolation that relies on PEP solvers. A solver based on rational interpolation (NLEIGS). MFN can be used to compute the action of a matrix function on a vector.
In numerical analysis, the ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method [1] while retaining the optimal [2] worst-case performance of the bisection method. [3]
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 ...
This product is a monic polynomial of degree n. It may be shown that the maximum absolute value (maximum norm) of any such polynomial is bounded from below by 2 1−n. This bound is attained by the scaled Chebyshev polynomials 2 1−n T n, which are also monic. (Recall that |T n (x)| ≤ 1 for x ∈ [−1, 1]. [5])
Aitken interpolation is an algorithm used for polynomial interpolation that was derived by the mathematician Alexander Aitken. It is similar to Neville's algorithm . See also Aitken's delta-squared process or Aitken extrapolation .