What is cubic polynomial interpolation?
What is cubic polynomial interpolation?
Cubic spline interpolation is a special case for Spline interpolation that is used very often to avoid the problem of Runge’s phenomenon. This method gives an interpolating polynomial that is smoother and has smaller error than some other interpolating polynomials such as Lagrange polynomial and Newton polynomial.
What is piecewise constant interpolation?
The piecewise-constant, left-endpoint interpolation is an example of a first-order scheme. If p = 2, we say the scheme is second-order accurate; for h sufficiently small, reduction of h by a factor of two will reduce the error by a factor of four. We shall shortly introduce an example of a second-order scheme.
How is a cubic Hermite interpolating polynomial defined?
On each subinterval x k ≤ x ≤ x k + 1 , the polynomial P ( x) is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points. P ( x) interpolates y , that is, P ( x j) = y j, and the first derivative d P d x is continuous.
What is the shape preserving piecewise cubic interpolation?
Shape-Preserving Piecewise Cubic Interpolation. pchip interpolates using a piecewise cubic polynomial with these properties: On each subinterval , the polynomial is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points.
How to calculate a piecewise cubic interpolating polynomial?
p = pchip (x,y,xq) returns a vector of interpolated values p corresponding to the query points in xq. The values of p are determined by shape-preserving piecewise cubic interpolation of x and y. pp = pchip (x,y) returns a piecewise polynomial structure for use with ppval and the spline utility unmkpp.
How does spline and pchip construct the same polynomial?
spline constructs in almost the same way pchip constructs . However, spline chooses the slopes at the differently, namely to make even continuous. This difference has several effects: spline produces a smoother result, such that is continuous.
