Question

Need help modifying my Matlab script below (myscript calculates the square root of a number. using a Newton-Raphson method with 1 as the initial guess, calculates true and estimated error, and shows each iteration).

-I need to create three new functions each of which should be called in the main script. These functions are needed to replace code that is currently in my script shown below.

-I need to create these functions:

A function to find f(x)

A function to find f '(x) ?

A function to determine the next guess, xn+1

-Need to plot estimated error vs iteration number, using both a marker and a line.

On the same plot, show actual error versus iteration, using different colors, markers, and line types.

Here are the functions I created:

%function to find f(x)

function x = func_eval(x_o,z)
x = (x_o)^2-z;

return

%function to find f'(x)
function x = deriv_eval(x_o)
x = 2*x_o;
return

 %next_val.m

 function x_new = next_val(x)
 if x == 0
     x_new = 1;
     return;

Here is my code without these functions implemented:

%Matlab script to calculate the square root of a number.

clear all;

close all;

clc;

z = input('Input a number to find square root:');

disp('Exact value is:')

x_o=1; %Initial guess of 1

disp(sqrt(z))

%Improved initial guess code

%  if z>=1

%      x_o = 1;

%      while (x_o)^2 < z

%       

%         x_o = x_o*10;

%      end 

%  x_o = x_o/2; 

%  else

%      x_o = 1;

%      while x_o^2> z

%          x_o = x_o/10;

%      end

%      x_o = x_o*2;

%  end

%  

         

 

tolerance_lim = 0.0000000001; % tolerance limit is 10 significant figures

i = 0; % iteration number

disp ('Iteration Number: ')

disp(i)

func_eval  = (x_o)^2-z;

deriv_eval = 2*x_o;

y = func_eval/deriv_eval;

x_new = x_o - y;

est_error = (x_new - x_o);

true_error =  sqrt(z)-x_o;

disp('Initial guess is:')

disp(x_o)

disp('Estimated error:')

disp(est_error)

disp('Exact error:')

disp(true_error)

func_eval  = (x_o)^2-z;

deriv_eval = 2*x_o;

y = func_eval/deriv_eval;

x_new = x_o - y;

est_error = (x_new - x_o);

while abs(est_error/x_o) >= tolerance_lim

    i = i+1;

 disp('Iteration Number:')

 disp(i)

 

x_o = x_new;

func_eval= (x_o)^2-z;

deriv_eval = x_o*2;

y = func_eval/deriv_eval;

x_new = x_o - y;

 

disp('Current guess is:')

disp( x_new)

est_error = x_new - x_o;

true_error =  sqrt(z)-x_new;

disp('Estimated error:')

disp(est_error)

disp('Exact error:')

disp(true_error)

end

disp('Converged!')