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Let g(a)=sf(a) be the function whose roots we seek to find, where f(a)
is an arbitrary function and s is a constant. If we find the roots of
g(a)=0, then we also have found the roots of f(a)=s. Newton's iteration for
g(a)=0 can be written as
g(a_{t})=g'(a_{t})(a_{t+1}a_{t}), or

sf(a_{t})=f'(a_{t})(a_{t+1}a_{t})

(1) 
If we now consider f(a)=a^{2}, then we can write (1) as:

sa_{t}^{2}=2a_{t}(a_{t+1}a_{t})

(2) 
which gives Newton's iterative procedure for finding square roots
 
(3) 
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Stanford Exploration Project
7/5/1998