Up: Kantorovitch theorem
Previous: Kantorovitch theorem
Let a system of equations in unknowns:
each being at least .
Let be a point and
, the norm being
Assume that is such that:
Then there is an unique solution of in and Newton method
used with as estimate of the solution will converge toward
this solution .
An interesting use of Kantorovitch theorem can be found in
- the Jacobian matrix of the system has an inverse
- the constants satisfy