The PCG process can be terminated
when either one of the following conditions is satisfied:
(1) The residual is sufficiently small, (2) the quadratic model
of eq. (34) is sufficiently reduced, or (3) a
direction of * negative curvature* is encountered
(i.e., ), possible
since may not be positive-definite.
Two effective truncation tests monitor the relative
residual norm (RT) [18] and the decrease of the quadratical model
(QT) [47].

The inner loop of a TN algorithm at Newton step **k** (step 2 of algorithm
2.4) can then be sketched as follows. For clarity, we omit the subscript
**k** from , , , ,
and **q**. The sequence
of vectors denotes the PCG iterates for ,
and a small positive number for the negative curvature test,
such as , is chosen, along with
appropriate values of or (for truncation), around 0.5.