Accuracy

Two criterion are used to determine if a box possibly includes a solution of the system:

• the largest width of the components of the box is lower than epsilon and the functions intervals for this box all contain 0
• the largest width of the function intervals is lower than epsilonf and they contain all 0. You must be aware that this test is only used if there is no inequality in the system. In that case it is compulsory to have an epsilon not equal to 0 otherwise the procedure may lead to an infinite loop.

If we use only the first criteria (i.e. we put epsilonf=0) the largest width of the solution intervals will be epsilon. A consequence is that the unknowns should be normalized in order that all the intervals in the TestDomain have roughly the same width.

If we use only the second criteria the width of the solution intervals cannot be determined and the functions should be roughly normalized (see the example in section 15.1.3 for the importance of the conditioning).