Question

Write a Matlab function for: 1. Root Finding: Calculate the root of the equation f(x)=x^3 −5x^2 +3x−7 Calculate the accuracy of the solution to 1 × 10−10. Find the number of iterations required to achieve this accuracy. Compute the root of the equation with the bisection method. Your program should output the following lines: • Bisection Method: Method converged to root X after Y iterations with a relative error of Z.

Answer 1

`Hey,

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clc
clear all
close all
format long
f = @(x) x^3-5*x^2+3*x-7;
e=1e-10;
a=-1;
b=5;
iter = 0;
  
if f(a)*f(b)>=0

disp('No Root')

else

prev = (a+b)/2;
p=a;
while (abs(f(p))>e)
prev=p;

iter =iter+ 1;

p = (a+b)/2;

if f(p) == 0
p
q=1
break;

end

if f(a)*f(p)<0

b = p;

else

a = p;

end
if(iter==100)
disp('the required accuracy is not reached in 50 iterations');
end
end

end
fprintf('Bisection Method: Method converged to root %.10f after %d iterations with a relative error of %.4e.\n',p,iter,abs(b-p)/abs(p));

Kindly revert for any queries

Thanks.