Let a system ,
the Jacobian matrix of this system and
a solution of the system.
The purpose of the
inflation method is to build a box that will contain only this solution.
Let
be a ball centered at
: if for
any point in
is not singular, then the ball contains only one
solution of the system.
The problem now is to determine a ball such for any point in the ball
the Jacobian is regular. Let be the matrix
whose
components are intervals. Let
be the diagonal element of H having
the lowest absolute value, let
be the maximum of the absolute
value of the sum of the elements at row
of
, discarding the
diagonal element of the row and let
be the maximum of the
's. If
, then the matrix is denoted diagonally dominant
and all the matrices
are regular [19].
Let be a small constant: we will build incrementally the
ball
by using an iterative scheme
defined as: