The 3B method is an usually efficient method
to reduce the width of the variable intervals. This method
can be used for any algorithm of `ALIAS`
and is embedded in the code of the solving procedures of the C++ library.

The principle of the method is quite simple. Let assume that we deal with a problem with variables and that the range for the variable is [] while is a small number. The procedure will examine if the problem may have a solution if the range for is reduced to [ ]. If it is not the case the range for may be reduced to []=[ ]. The procedure will then be repeated by using as a new value for until the algorithm either determine that there is no solution to the problem or fails to show that that is no solution for the range [ ]. The algorithm will then try to reduce the range for on the "right" side i.e. by examining if the problem has no solution for the range [ ]. This process is repeated in turn for each variable.

Within Maple the value of is given by the variable
``ALIAS/Delta3B`` which set an identical value of for
all variables. Alternatively you may specify a specific value of
for each variable by assigning a list to the variable
``ALIAS/Delta3B_ARRAY`` with as many elements as unknowns: each
element of this list is the value of for each variable.

The 3B method will not be used for variables whose range have a width
greater than a given threshold. This threshold is defined by the
variable ``ALIAS/Max3B`` (default value: 5). You may assign a new
value for this threshold by:

`ALIAS/Max3B`:=10:Alternatively you may specify a specific threshold for each variable by using the array

`ALIAS/Max3B_ARRAY:=array([0.1,0.1,0.05]):indicates that the 3B method will be used only if the width or the input intervals is lower than 0.1 for the 2 first unknowns and 0.005 for the third one.

As soon as the `Max3B, Delta3B` values have been set you activate
the 3B method by setting the
``ALIAS/3B`` variable to 1 or 2.
At iteration of the 3B method the algorithm will try to
reduce the range for the variable by . Assume that is
larger than 1 and the algorithm fails:

- if
``ALIAS/3B``is set to 1 the algorithm will move to the next variable (or try to reduce the range on the "right" side if we dealing with the "left" side) - if
``ALIAS/3B``is set to 2: the algorithm was considering for the variable the range [ ] when it has failed. Instead of moving to the next step the algorithm will consider the range [ ] and repeat the process until the method fails for a gain exactly equal to