TryNewton

This procedure will create a C++ program that is intended to be used within an equation solving procedure as a simplification procedure. For each call to this program the program will run at most newton_iteration iterations of the classical Newton scheme with as initial guess for the solution the mid-point of the interval vector that is the argument of a simplification procedure. If Newton seems to converge (i.e. the residues have a width lower than fepsilon) the program first checks that the approximation of the root lies within a given search domain and then uses the Kantorovitch theorem and the epsilon-inflation scheme to certify that there is a single solution within a given ball. In that case the program will return 11, otherwise it returns 0. The general use of this procedure is for finding quickly a root of the system although in some cases it may speed up the process of finding all solutions of the system.

The syntax of this procedure is

 
TryNewton(func,vars,Init,procname)

• func: a list of n equations
• vars: a list of n unknowns names
• Init: a search domain for the solutions
• procname: the name of the simplification program that will be written in the file procname.C

This procedure may be used with GeneralSolve and GradientSolve. It should not be used with HessianSolve as the corresponding C++ program is already embedded in the C++ code of this procedure.