Page 84 - Numerical Analysis Using MATLAB and Excel

Solutions to End-of-Chapter Exercises

2.
a. We will use the for end loop MATLAB program and specify 12 iterations. Before we write
the program script, we must define a function assigned to the given polynomial and save it
as a function m−file. We will define this function as exercise2 and will save it as

exercise2.m

function y= exercise2(x);
y = x .^ 4 +x − 3;
After saving this file as exercise2.m, we execute the following program:

x1=1; x2=2; % x1=a and x2=b
disp(' xm fm') % xm is the average of x1 and x2, fm is f(xm)
disp('-------------------------') % insert line under xm and fm
for k=1:12;
f1=exercise2(x1); f2=exercise2(x2);
xm=(x1+x2) / 2; fm=exercise2(xm);
fprintf('%9.6f %13.6f \n', xm,fm)% Prints xm and fm on same line;
if (f1*fm<0)
x2=xm;
else
x1=xm;
end
end
MATLAB displays the following:

xm fm
-------------------------
1.500000 3.562500
1.250000 0.691406
1.125000 -0.273193
1.187500 0.176041
1.156250 -0.056411
1.171875 0.057803
1.164063 0.000200
1.160156 -0.028229
1.162109 -0.014045
1.163086 -0.006930
1.163574 -0.003367
1.163818 -0.001584
b. We will use the while end loop MATLAB program and specify a tolerance of 0.00001.

We need to redefine the function m−file because the function in part (b) is not the same as
in part a.

Numerical Analysis Using MATLAB® and Excel®, Third Edition 2−31
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