My Learning Blog

The 1×1 strategy is sufficient for detecting boundary errors and the Nx1 strategy is effective foretermining exactly what type of boundary error is present, where N is the dimension of the input space.  The 1×1 strategy tests two points for each boundary inequality, one on the boundary and one off the boundary.  The two points are chosen as close as possible to one another to ensure that domain shift errors are properly detected. If two domainsshare a boundary, then the off point is always in the domain that is open with respect to that boundary.

The Nx1 strategy tests N+1 points for each boundary inequality, N points on the boundary and 1 point off the boundary. The off point is chosen at or near the centroid of the on points. One must always be careful to choose the off point so that it is in a valid domain, i.e. one that leads to valid computations or to a specific error condition, otherwise the point may be
rejected for coincidental reasons, e.g. by an initial analysis that rejects all points not in a domain that leads to subsequent processing.