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Piecewise Hermite Cubic Interpolation

version (2.24 KB) by Juan Camilo Medina
Interpolates with a Hermite cubic polynomial using the function values and corresponding derivatives


Updated 11 Apr 2011

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Piecewise Hermite cubic interpolation between 2 points knowing derivative values

Syntax: y=p3hermite(x,pointx,pointy,yprime,plt)
pointx = data points of the independent variable
(The points do not have to be equally spaced)
pointy = data points of the dependent variable. pointy is the value of
the function at pointx
yprime = data points of the dependent variable's derivative. yprime is the
derivative of the function at pointx
x = an arbitrary vector that will be interpolated
plt = If plt is a number greater than 0 it will plot the interpolation
employing the number in plt as handle for the figure

-This function returns the piecewise interpolation "y" of a vector "x".
The algorithm employs two adjacent points (from pointx) and interpolates
with a Hermite cubic polynomial using the function values and the corresponding derivatives.
-pointx, pointy, and yprime must be vectors with the same number of elements.
"x" and "y" have the same number of elements.

Written by Juan Camilo Medina 2011

Suppose you have the values of a function "y(x)" at the points xi={0,4,9},
those are yi={2,-2,sqrt(2)} respectively. You also know the values of the
derivative of y(x) at the same points (pointx) yi'=[0,0,-pi/(2*sqrt(2))] respectively.
You want to interpolate within those values with an arbitrary vector "x"
using piecewise cubic Hermite polynomials

pointy=[2,-2,sqrt(2)]; %function values at pointx
yprime=[0,0,-pi/(2*sqrt(2))]; %derivative of the function at pointx
x=0:0.01:pointx(end); % arbitrary vector to be interpolated
y_ex=2*cos(pi/4*x); % exact value (y corresponds to y=2*cos(pi/4*x))
plot(x,y_ex,'--k'); axis tight; % plots exact solution for comparison
legend('Interpolation Points','Hermite Interpolation','Exact Value','Location','Southeast')

Written by Juan Camilo Medina - The University of Notre Dame

Cite As

Juan Camilo Medina (2022). Piecewise Hermite Cubic Interpolation (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Lagrange polynomial interpolation

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