Quadratic/Cubic versus Linear interpolations - Free
abrobecker.free.fr/text/quad.htmQuadratic interpolation is made with polynomials of degree two, while cubic uses degree 3 polynomials. So the derivative of the quadratic functions will be a succession of connected segments (french mathematicians would tell the derivative is "affine par morceaux") while the derivative of the cubic interpolation will be composed of connected quadratic functions.
METHOD OF QUADRATIC INTERPOLATION
people.math.sc.edu › Quadratic_InterpolationMETHOD OF QUADRATIC INTERPOLATION KELLER VANDEBOGERT 1. Introduction Interpolation methods are a common approach to the more general area of line search for optimization. In the case of quadratic inter-polation, the function’s critical value is bracketed, and a quadratic interpolant is tted to the arc contained in the interval. Then, the
Polynomial interpolation - Wikipedia
https://en.wikipedia.org/wiki/Polynomial_interpolationPolynomials can be used to approximate complicated curves, for example, the shapes of letters in typography, given a few points. A relevant application is the evaluation of the natural logarithm and trigonometric functions: pick a few known data points, create a lookup table, and interpolate between those data points. This results in significantly faster computations. Polynomial interpolation also forms the basis for algorithms in numerical quadrature and numerical ordinary …