Question

my w it uld Ul Table 2.10. Problem 3 (Chapter 3) - [Parts (a) and (b) are independent] a) For the function f(x) = x-exp(-x), do a calculation by hand using a calculator to find the root to - an accuracy of 0.1. At most, five iterations (or fewer) are needed to obtain the desired accuracy. (b) Write a program which uses the bisection method to find the root of the function f(x) = 5 - x on the interval [a, b] = [0.1, 0.25). Use Eq. (3.2) of Theorem 3.1 ("Bisection Convergence and Error") to determine a priori the number of steps necessary for the root accuracy to within 10

Answer 1

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clc;
clear all;

f=@(x)5-x^(-1); %function

a=0.1;b=0.25; % interval

if(f(a)*f(b)>0)
fprintf('Root is not applicable in [%f, %f]\n',a,b)
else
tol = 1e-6; % tolerance

Nmax=100;
err=0.1;
niter=0;

while (err >= tol && niter<=Nmax )
x = (a + b)/2;
if ( f(x) == 0 )
break;
elseif ( f(a)*f(x) < 0 )
b = x;
else
a = x;
end
  
err=abs( (b-a)/2)*100;
niter=niter+1;
Tf(niter)=x;
end

end
% x is root
%niter is number of iteration
disp('Root of the function')
x
disp('Number of iteration')
niter

%%%%%%%%%%%%%%%% Solution

Root of the function

x =

0.199999994039536

Number of iteration

niter =

23

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