My code isnt looping until answer is found

function [n] = NEWTON(x,err)



	f1=@(x)(-9*x^5-8*x^3+12);
    f2=@(x)(45*x^4-24*x^2);
    %use equation
 
          xnew = x - (f1(x)/f2(x));
    %evaluate
   if abs((xnew - x )/xnew) > err
       xs = xnew;
   
   else    
   x = xnew;
   end


  
fprintf('The optimization estimate is=%f', xs);
end

I am trying to use newtons mathod to find the iptimization estimate, but it is only doing one iteration and then stopping, I am unsure how I can make it go until the answer is there within the error limit.

Answer 1

[KALYAN ACHARJYA]

% I am certain that you can use while loop here, Lets say new evaluated error in each iterations names as error_update

and err is err defined during pass the function input values, i.e. error limit

while err_update<err
%your code
end

Please ensure that the err_update is increasing in each iteration, so that loop does not run forever.

function [n]=NEWTON(x,err)
f1=@(x)(-9*x^5-8*x^3+12);
f2=@(x)(45*x^4-24*x^2);
err_update=0; %Initialization
while err_update<err  %here err is user defined error limit
%use equation 
xnew = x - (f1(x)/f2(x));
err_update=abs((xnew - x )/xnew);
x=xnew;
end
fprintf('The optimization estimate is=%f', xs);
end

Please change the required inside while loop. Hope it helps!

[Anthony Ming]

Unfortunately I am still getting the same answer as before, I noticed you said to change the required inside while loop, could you explain that?

Also thank you very much for helping me

[KALYAN ACHARJYA]

What input you have passed to the function, please provide details?

[Anthony Ming]

In my book, there is an answer that I know is right so i checked it but had to change f1 and f2.

f1=@(x)2*cos(x)-(x/5);

f2=@(x)-2*sin(x)-(1/5);

and i used NEWTON(2.5,.001)

The answer should be around 1.42755

[KALYAN ACHARJYA]

@Anthony, I dont know which book you are talking about. I have answer based on your heading question. I have trued with new f1 and f2 also its giving me different answer.

function [n]=NEWTON(x,err)
f1=@(x)(2*cos(x)-(x/5));
f2=@(x)(-2*sin(x)-(1/5));
err_update=0; %Initialization
while err_update<err  %here err is user defined error limit
%use equation 
xnew=x-(f1(x)/f2(x));
err_update=abs((xnew-x)/xnew)
x=xnew;
end
fprintf('The optimization estimate is=%f', xnew)
end

Here results

>> NEWTON(2.5,.001)
xnew =
    0.9951
err_update =
    1.5124
The optimization estimate is=0.995082>> 

The issue with concept/coding (maths) logic, see the while loop failed in first iterations

err_update=0;
while loop true as 0<0.001

Next iterations

while err_update=1.5124<0.001 % Condition false

no ierations and jump to fpintf statemnet.

Hope you getting the clue!