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Piecewise Hermite cubic interpolation between 2 points knowing derivative valuesSyntax: y=p3hermite(x,pointx,pointy,yprime,plt)Wherepointx = 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 pointxyprime = data points of the dependent variable's derivative. yprime is the derivative of the function at pointxx = an arbitrary vector that will be interpolatedplt = 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 interpolateswith 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 2011Example: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 thederivative 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 polynomialsThus:pointx=[0,4,9];pointy=[2,-2,sqrt(2)]; %function values at pointxyprime=[0,0,-pi/(2*sqrt(2))]; %derivative of the function at pointxx=0:0.01:pointx(end); % arbitrary vector to be interpolatedy=p3hermite(x,pointx,pointy,yprime,2);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 comparisonlegend('Interpolation Points','Hermite Interpolation','Exact Value','Location','Southeast')Written by Juan Camilo Medina - The University of Notre Dame
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Windows Software
Albina Merfyn - I find this to be really easy to use. I can...
