Page 85 - Numerical Analysis Using MATLAB and Excel

Chapter 2 Root Approximations

function y= exercise2(x);
y = sqrt(2.*x+1)−sqrt(x+4);
After saving this file as exercise2.m, we execute the following program:

x1=2.1; x2=4.3; tol=0.00001; % If we specify x1=a=2 and x2=b=4, the program
% will not display any values because xm=(x1+x2)/2 = 3 = answer
disp(' xm fm'); disp('-------------------------')
while (abs(x1-x2)>2*tol);
f1=exercise2(x1); f2=exercise2(x2); xm=(x1+x2)/2;
fm=exercise2(xm);
fprintf('%9.6f %13.6f \n', xm,fm);
if (f1*fm<0);
x2=xm;
else
x1=xm;
end
end
When this program is executed, MATLAB displays the following:

xm fm
-------------------------
3.200000 0.037013
2.650000 -0.068779
2.925000 -0.014289
3.062500 0.011733
2.993750 -0.001182
3.028125 0.005299
3.010938 0.002065
3.002344 0.000443
2.998047 -0.000369
3.000195 0.000037
2.999121 -0.000166
2.999658 -0.000065
2.999927 -0.000014
3.000061 0.000012
2.999994 -0.000001
3.000027 0.000005
3.000011 0.000002

2−32 Numerical Analysis Using MATLAB® and Excel®, Third Edition
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