  The initialization of equation-based differential-algebraic system models,
and more in general the solution of many engineering and scientific problems,
require the solution of systems of nonlinear equations. Newton-Raphson's method
is widely used for this purpose; it is very efficient in the computation of the
solution if the initial guess is close enough to it, but it can fail otherwise.
In this paper, several criteria are introduced to analyze the influence of the
initial guess on the evolution of Newton-Raphson's algorithm and to identify
which initial guesses need to be improved in case of convergence failure. In
particular, indicators based on first and second derivatives of the residual
function are introduced, whose values allow to assess how much the initial
guess of each variable can be responsible for the convergence failure. The use
of such criteria, which are based on rigorously proven results, is successfully
demonstrated in three exemplary test cases.
