MATLAB: Question regarding while loop

loopMATLABwhile loop

function y = approx_sqrt(x)
y = x;
while abs(y^2 - x) > 1e-7*x
    y = (x/y + y)/2
This is part of the code in my lecture class. I wonder what is the purpose of setting y = x at the begining?
Can anyone explain to me? Thank you so much.

Best Answer

(1) Because you need a value in the logic test: abs(y^2 - x) > ...
(2) Because you need an initial guess on the right-hand side of the Newton-Raphson expresssion: (x/y + y)/2
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