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Let g(a)=s-f(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(at)=-g'(at)(at+1-at), or
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s-f(at)=f'(at)(at+1-at)
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(223) |
If we now consider f(a)=a2, then we can write () as:
which gives Newton's iterative procedure for finding square roots
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Stanford Exploration Project
7/5/1998