It is shown that the contraction mapping principle with the involvement of a Carleman Weight Function works for a Coefficient Inverse Problem for a 1D hyperbolic equation. Using a Carleman estimate, the global convergence of the corresponding numerical method is established. Numerical studies for both computationally simulated and experimentally collected data are presented. The experimental part is concerned with the problem of computing dielectric constants of explosive-like targets in the standoff mode using severely underdetermined data.

翻译：显示在Carleman Weight 函数参与下进行的收缩映射原则为 1D 双曲方程式的 Covale 逆向问题工作。 使用Carleman 估计, 相应数字方法的全球趋同得到确定。 提供了计算模拟数据和实验收集数据的数值研究。 实验部分涉及使用严重低于定数的数据在对齐模式下计算类似爆炸目标的电离常数的问题。