  In this paper, an idea to solve nonlinear equations is presented. During the
solution of any problem with Newton's Method, it might happen that some of the
unknowns satisfy the convergence criteria where the others fail. The
convergence happens only when all variables reach to the convergence limit. A
method to reduce the dimension of the overall system by excluding some of the
unknowns that satisfy an intermediate tolerance is introduced. In this
approach, a smaller system is solved in less amount of time and already
established local solutions are preserved and kept as constants while the other
variables that belong to the "set" will be relaxed. To realize the idea, an
algorithm is given that utilizes applications of pointers to reduce and
evaluate the sets. Matrix-free Newton-Krylov Techniques are used on a test
problem and it is shown that proposed idea improves the overall convergence.
