Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Pliska Studia Mathematica Bulgarica, Vol. 12, No 1, (1998), 31p-38p
Abstract:
Based on the original proof of the Graves theorem [9] we study the convergence of
the Newton method for the solution of the equation f (x) = y, uniform with respect
to the starting point and the parameter y. We show that the surjectivity of the
Jacobian implies the Aubin continuity, relative to the supremum norm, of the map
taking the starting point and the parameter y to the set of all Newton sequences.
These results complement our previous paper [4].
