Question

(12 points) Use polynomial interpolation and central difference techniques to compute f and f at x 0.5 using the following unequally spaced data. 1.0 0.0 2.0 f(x) 15.0 2.0 11.0 Hint: fit a parabola through the three data points.

Please solve using matlab and show your work so I can see where I am going wrong. Your help is appreciated

Answer 1

clear
clc
x=[-2 0 1];
f=[15 11 2];
fit=polyfit(x,f,2);
X=-5:.1:5;%we will now evaluate fitted parabola at these points, with a gap of .1
Y=polyval(fit,X);%evaluated
[~,index]=find(X==.5);%finding index where x=.5;
fdash=(Y(index+1)-Y(index-1))/(2*.1)
fDoubledash=(Y(index-1)-2*Y(index)+Y(index+1))/(.1*.1)

Command Window fdash- -9.0000 EDoubledash - -4.6667