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Let a system of equations in unknowns:
each being at least .
Let be a point and
, the norm being
.
Assume that is such that:
 the Jacobian matrix of the system has an inverse
at
such that


for
and
 the constants satisfy
Then there is an unique solution of in and Newton method
used with as estimate of the solution will converge toward
this solution [3].
An interesting use of Kantorovitch theorem can be found in
section 2.5.
JeanPierre Merlet
20121220