To explain Fig. 10, we present the GLK equation (56) as
w(z, t) − CF (X) 2 z −zf (t − τ )w(z, τ )dτ = 1 2 , t ∈ [−z, z], ∀z ∈ [0, T /2].(61)
In (61) f (t) is the pre-preprocessed **data** as in in subsection 2.3.1 andf (t) is the odd extension of f (t). Denote β := z · CF (X) sup |t|<T /2 f (t) . If β ∈ (0, 1), then one can solve integral equation (61) via the resolvent series, see, e.g. the book [35]. It is clear from this series that the solution w(z, t) changes almost with an exponential speed when the calibration factor CF (X) changes. This explains, at least partially, the exponential behavior of GLK curves of Fig. 10. This is because the **data** for the inverse problem are introduced in the operator. On the other hand, almost linear behavior of AGCM curves on Fig. 10 can be explained by the fact that AGCM uses the logarithm of the solution w of the problem (13), (14), see (18).
