This procedure allows one to take into account the specific structure
of the system to solve when using the interval Newton method. In this
method the classical algorithm, for example used by default in `GradientSolve` or `HessianSolve`, computes numerically for a box the interval evaluation
of
where is the mid-point of . This
numerical calculation does not allow to to take into account the
dependency between the elements of when computing . This
procedure compute symbolically the matrix and re-arrange its
elements (with `MinimalCout`) in order to reduce the dependency
problem.

The syntax of this procedure is

IntervalNewton(func,nfunc,funcproc,njfunc,Jfuncproc,typemid,grad,grad3B,incl,vars,procname)where

`func`: the list of equations,`nfunc`: the number of equations that will be evaluated by`funcproc`. It may not be the same than the number of equations in`func``funcproc`: the name of the procedure that is used to evaluate the equations. It may be the name of a procedure designed by the end-user with`MakeF`or the name of the procedure that will be used by the solving algorithm (usually`"F"`)`njfunc`: the number of equations that will be used when computing the derivatives. It may not be the same than the number of equations in`func``Jfuncproc`: the name of the procedure that is used to evaluate the derivative of the equations. It may be the name of a procedure designed by the end-user with`MakeJ`or the name of the procedure that will be used by the solving algorithm (usually`"J"`)`typemid`: the interval Newton method uses a conditioning matrix. This flag will indicate which type of conditioning matrix is used. If 0 we use , if 1 , if 2 both above conditioning matrices will be used`grad, grad3B`: it is possible to use the derivatives of to improve the interval evaluation. If`grad`is set to 1 this will be used for all boxes in the algorithm. If`grad3B`is set to 1 it will also be used for the sub-boxes that are considered when using the`3B`method`incl`: a list. If the end-user uses a specific procedure to compute the interval evaluation of`func`, then`incl[1]`should be set to 1. Similarly if it uses its own procedure to compute the derivatives of`func`, then`incl[2]`should be set to 1.`vars`: the list of variables. All unknowns in the elements of`func`must appear first in this list`ProcName`: the name of the simplification procedure that will be created in the file`ProcName.C`