Can't figure out what I am doing wrong. Looking to find square root using the equation given x=(x+x/a)/2. I also feel like I am not making use of the approximation errors ea and es.

Having trouble determining what I am doing wrong. I don't feel like I am initiallizing x incorrectly, because that is what I am trying to solve for. Not sure if I am making use of ea and es error approximations as well.

code is as follows:

clear
a=input('Enter Number'); %User input number
x=sqrt(a);
ea=100;     %approximate relative error 100 percent 
es=0.01;  %stopping point for error must be less than
count=1;  %iteration beginning 
countmax=1000;  %max number of iterations allowed 
if 0<a          %must be positive number
  while (count<countmax) && (es<ea) %How is es/ea even a factor???
    x=(x+(a/x))/2;    %equation to solve for square root
    disp(x);          %show answer
    x_old=x;
    ea=((x-x_old)/x)*100;
    count=count+1;
  end
else
    msgbox("Enter Positive Number")   %number entered not positive
end 

Answer 1

[Matt J]

You need to take absolute values,

ea=abs((x-x_old)/x)*100;

Answer 2

[James Tursa]

You can't do these assignments in this order:

    x_old=x;
    ea=((x-x_old)/x)*100;

The first one will cause the second one to always be exactly 0. You need to reverse the order of these equations (with the abs( ) that Matt J points out):

    ea=abs((x-x_old)/x)*100;    
    x_old=x;

Because of that, you will need to initialize x_old prior to the start of the loop:

    x_old = x;

And, it is quite unfair to start your iteration process at exactly the answer. So this line needs to be replaced:

    x = sqrt(a);

Pick something else. For simplicity, maybe just

    x = a;

Answer 3

[Stijn Haenen]

just use this to solve x=(x+x/a)/2

a=input('')
syms x
xsol=vpasolve(x==(x+x/a)/2,x)

[N/A]

Thank you for the help, but this just returns x not a value for x. Even using the initial equation I had an using syms x I get the equation with x left in place versus an inputted a and returns an x value that should be the square root of a.

[James Tursa]

@Stijn: The original question is not asking how to solve an algebraic equation for x, but how to fix the iterative code for calculating the sqrt of a number. Two completely different things.