Page 76 - Numerical Analysis Using MATLAB and Excel

The Bisection Method for Root Approximation

end

The commands between while and end are executed as long as all elements in expression are
true. The script should be written so that eventually a false condition is reached and the loop
then terminates.

There is no need to create another function m−file; we will use the same as in part a. Now we
type and execute the following while end loop program.

x1=1; x2=2; tol=0.00001;
disp(' xm fm'); disp('-------------------------')
while (abs(x1-x2)>2*tol);
f1=funcbisect01(x1); f2=funcbisect01(x2); xm=(x1+x2)/2;
fm=funcbisect01(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
-------------------------
1.500000 17.031250
1.250000 4.749023
1.125000 1.308441
1.062500 0.038318
1.031250 -0.506944
1.046875 -0.241184
1.054688 -0.103195
1.058594 -0.032885
1.060547 0.002604
1.059570 -0.015168
1.060059 -0.006289
1.060303 -0.001844
1.060425 0.000380
1.060364 -0.000732
1.060394 -0.000176
1.060410 0.000102
1.060402 -0.000037
1.060406 0.000032
1.060404 -0.000003

Numerical Analysis Using MATLAB® and Excel®, Third Edition 2−23
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