  A regularized $\alpha-$system of the Nonlinear Schr\"{o}dinger Equation (NLS)
with $2\sigma$ nonlinear power in dimension $N$ is studied. We prove existence
and uniqueness of local solution in the case $1 \le \sigma <\frac{4}{N-2}$ and
existence and uniqueness of global solution in the case $1 \le \sigma <
\frac{4}{N}$. When $\alpha \to 0^+$, this regularized system will converge to
the classical NLS in the appropriate range. In particular, the purpose of this
numerical regularization is to shed light on the profile of the blow up
solutions of the original Nonlinear Schr\"{o}dinger Equation in the range
$\frac{2}{N}\le \sigma <\frac{4}{N}$, and in particular for the critical case
$\sigma = \frac{2}{N}$.
