Question

Page 73, as mentioned in the stated question, is provided below

1. Consider a new root-finding method for solving f(x) = 0. Successive guesses for the root are generated from the following recurrence formula: Xn+1 = In f(xn) fhen + f(xn)] – F(Xn) (1) Write a user-defined function with the function call: [r, n] = Root fun (f, xl, tol, N) The inputs and outputs are the same as for the user-defined function Newton described on page 73 of Methods. The inputs tol and N should be optional, as for Newton, with the same default values.

Answer 1

function [r, n]=newtnfun(f,x1,tol,N)
%f function

% %tol stoping criterior
% % x1 initial value
% f=@(x)exp(sin(x).^3)+x.^6-2*x.^4-x.^3-1;

x(1)=x1; % initial guess
n=1;
ebs=0.1; % Intial error
while(ebs>tol& n<N)

x(n+1)=x(n)-(f(x(n))/(f(x(n)+f(x(n)))-f(x(n)))); %newton method

ebs=abs((f(x(n))/df(x(n))));
erorr(n)=ebs;

n=n+1;
if(n>=max_iter)
fprintf('not converge')
end
end
r=x(n+1);
end