Question

In Matlab,

Construct the natural cubic spline (see the LiveScript) to interpolate the Runge function (see Homework 6) using 10, 15, 20, and 25 equispaced nodes.

Answer 1

MATLAB Code:

close all
clear
clc

xx = linspace(-1, 1, 1000);
yy = 1 ./ (1 + 25*xx.^2);
figure, hold on
plot(xx, yy), xlabel('x'), ylabel('f(x)')
title('Cubic Spline Interpolation')

N = [10 15 20 25];
for i = 1:length(N)
n = N(i);
x = linspace(-1, 1, n);
f = 1 ./ (1 + 25*x.^2);
yy = spline(x, f, xx);
plot(xx, yy)
end
legend('Actual Function', 'N = 10 nodes', 'N = 15 nodes', 'N = 20 nodes', 'N = 25 nodes')

Plots:

Cubic Spline Interpolation N-15 nodes N 20 nodes 80s 0.3

Zoomed versions of the above plot:

Cubic Spline Interpolation N-15 nodes N 20 nodes 0.85 08 0.75 0.1 0.1 ง.05

Cubic Spline Interpolation N-15 nodes N 20 nodes 0.79 0.78 0.77 0.78 0.76 0.74 0.73 0.72 0.09 0.125 0.1