论文标题
单个测量数据的1D双曲线系数逆问题的凸化
Convexification for a 1D Hyperbolic Coefficient Inverse Problem with Single Measurement Data
论文作者
论文摘要
提出了用于1D双曲线PDE系数逆问题的凸化数值方法的版本。该问题的数据是由单个测量事件生成的。该方法在全球收敛。结构中最重要的要素是加权Tikhonov样功能中卡尔曼的重量功能的存在。该功能严格凸出在希尔伯特空间中的某个有限集中，该集合的直径是任意的正数。建立了梯度投影方法的全局收敛性。计算结果证明了用于嘈杂数据的数值方法的良好性能。
A version of the convexification numerical method for a Coefficient Inverse Problem for a 1D hyperbolic PDE is presented. The data for this problem are generated by a single measurement event. This method converges globally. The most important element of the construction is the presence of the Carleman Weight Function in a weighted Tikhonov-like functional. This functional is strictly convex on a certain bounded set in a Hilbert space, and the diameter of this set is an arbitrary positive number. The global convergence of the gradient projection method is established. Computational results demonstrate a good performance of the numerical method for noisy data.
