Hence, a rigorous definition of the "approximate global convergence" property was introduced in [6,9,24,25]. In simple terms, it means that first an approximate mathematical model is introduced. The approximation of AGCM is a mild one: it amounts to the truncation of an asymptotic series with respect to 1/s, s → ∞, where s > 0 is the parameter of the Laplace transform with respect to t of the above hyperbolic PDE. This truncation is done only on the first iteration. Next, a numerical method is developed within the framework of the resulting mathematical model. Next, a theorem is proved, which claims that this method delivers a good approximation for the exact solution of that CIP without any a priori knowledge of a small neighborhood of that solution. The common perception of global convergence is that one should obtain correct solution if iterations would start from almost any point. That theorem claims, however, that a small neighborhood of the exact solution is achieved if iterations would start not from any point but rather from a function which can be obtained without any knowledge of that small neighborhood. That theorem was confirmed in numerical studies of both computationally simulated and experimental data. 3-d experimental **data** were treated in [8,6,20]. In particular, the most difficult blind **data** case was considered in [6,20,24]. We refer to the paper [29] and references cited there for another non-local method for a coefficient inverse problem.