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

%Matlab function for Bisection Method
clear all
close all

%function for which root have to find
fun=@(x) x.^3-5*x.^2+3*x-7;
fprintf('function for which root have to find\n')
disp(fun)

x0=0; x1=10; tol=10^-10;
[root,iter]=bisection(fun,x0,x1,tol);
fprintf('Method converged to root %f after %d iterations with a relative error of %e.\n',root,iter,tol)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [root,iter]=bisection(fun,x0,x1,tol)
  
    if fun(x0)<=0
        t=x0;
        x0=x1;
        x1=t;
    end
    %f(x1) should be positive
    %f(x0) should be negative
    k=10; count=0; maxit=1000;
    while k>tol
        count=count+1;
        xx(count)=(x0+x1)/2;
        mm=double(fun(xx(count)));
        if mm>=0
            x0=xx(count);
        else
            x1=xx(count);
        end

        %err(count)=abs(fun(x1));
        k=abs(fun(x1));
        %k=abs(x0-x1);
        if count>=maxit
            break
        end
    end
    root=xx(end);
    iter=count;
end

%%%%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%