Abstract:
In this paper we investigate the behavior of the misfit functional for a one-dimensional hyperbolic inverse
problem when an unknown coefficient stands by a lowest term of a differential equation. Assuming an existence
of an inverse problem solution we prove a uniqueness of a stationary point of the functional. If the minimization sequence belongs to a bounded set, we show that the following estimates of the convergence rate for the suggested method of the descent
$$
J[q_k]\le J[q_0]\exp\{-c(k-1)\},\quad\|q_k-q_*\|^2_{L_2[-T,T]}\le CJ[q_0]\exp\{-c(k-1)\}
$$
takes place.
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