非均匀时间网格上散点测量正则化的分数波动方程逆问题数值分析
数值分析
2025-06-25 v1 数值分析
摘要
本文旨在从终端数据重建未知初始值。我们在非均匀时间网格上构建分数波动方程的数值框架，置于较低的正则性假设下。随后，我们引入一种正则化方法，有效处理被随机噪声污染的散点测量。最终的随机收敛误差估计不仅平衡了离散误差、噪声以及观测点数的关系，还提出了正则化参数的先验选择。最后， presented several numerical experiments to demonstrate the efficiency and accuracy of the algorithm. 算法的效率与准确性。
引用
@article{arxiv.2506.18948,
title = {Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations},
author = {Dakang Cen and Zhiyuan Li and Wenlong Zhang},
journal= {arXiv preprint arXiv:2506.18948},
year = {2025}
}
备注
27 pages. arXiv admin note: text overlap with arXiv:2506.17575