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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.
Jean-Pierre Merlet
2012-12-20