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In many applications, for many reasons,
we have a starting guess of the solution.
You might worry that
you could not find the starting preconditioned variable
because you did not know the inverse of .The way to avoid this problem is to
reformulate the problem
in terms of a new variable where
.Then
becomes
or
Thus we have accomplished the goal of taking
a problem with a nonzero starting model
and converting it a problem of the same type
with a zero starting model.
Thus we do not need the inverse of because the iteration starts from so .

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Stanford Exploration Project

4/27/2004