Problem Three Write a MATLAB function that given a set of x values (r1) and the

Question

Problem Three Write a MATLAB function that given a set of x values (r1) and the corresponding values of f(zl) for some other function. f, and a second set of points r2, do a piece-wise linear interpo- lation of the function from the ri points to the z2 points. For example, let x1 C0:0.5:7] y sin x1); x2 C-1:0.05:8) then the function should return a piece wise linear approximation of the sin function evaluated at the points z2. That is you should be able to run plot (x2,z) where z is computed by your function, and see an piece-wise linear approximation of a sin curve. Turn in your solution, it must work for any function and sets of points z1 and r2 and cannot be based on similar built-in MATLAB functions.

Explanation / Answer

%piecewise.m

function y = piecewise( fx,x1,x2 )
    y = interp1(x1,fx,x2);
    return;
end

%CALLING SCRIPT

clc;
close all;
clear all;

x1 = 0:0.5:7;
x2 = -1:0.05:8;

fx1 = sin(x1);

z = piecewise(fx1,x1,x2);

plot(x2,z);

for i = 1:1:9;
   
    N = 2^i
    x1 = -1:1/N:1;
    x2 = -1:1/(10*N):1;
    fx2 = 1./(1+(25*(x1.^2)));

    strtitle = sprintf('N = %d',N);

    figure
    z = piecewise(fx2,x1,x2);

    plot(x2,z);
    title(strtitle);

    fx2 = 1./(1+(25*(x2.^2)));
    for j = 1:1:length(x2)
        diff(j) = abs(fx2(j)-z(j));
    end

    MAXDIFF(i) = max(diff);

end
MAXDIFF

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