On the choice of initial guesses for the Newton-Raphson algorithm.

• Only the initial guesses of variables affecting the Jacobian of a nonlinear system of equations influence the convergence of Newton's method. • Sufficient conditions for the reduction of the residuals after the first iteration of Newton's method are given. • Numerical indicators are defined to highlight which initial guesses of Newton's method are farthest from the solution. • Criteria based on those indicators are given to identify which initial guesses should be corrected in case of convergence failure of Newton's method • The criteria require the computation of the Jacobians and Hessians of the nonlinear equation residuals and are applicable to any system of equations. 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. [ABSTRACT FROM AUTHOR]