AI 中文总结
针对带精确数据的离散椭圆逆系数问题，研究人员开发了带显式残差准则的局部收敛算法及全局化变体，后者可在有限次全局搜索后切换至局部收敛算法，解决了数值求解器依赖良好初始值的问题。
AI 中文摘要
我们研究由椭圆逆系数问题（如Calderón问题，含有限测量值与未知量）的有限元离散化产生的有限维非线性逆问题。这类逆系数问题因非线性和不适定性而臭名昭著，数值求解器往往高度依赖良好的初始值。本研究中，我们开发了一种带显式残差准则的局部收敛算法，该准则可确保收敛至逆问题的解；还开发了其全局化变体，该变体保证能在有限次全局搜索步骤后自动切换至更快的局部收敛算法。
英文摘要
We consider finite-dimensional nonlinear inverse problems arising from finite element discretizations of elliptic inverse coefficient problems such as the Calderón problem with finitely many measurements and unknowns. Such inverse coefficient problems are notorious for their nonlinearity and ill-posedness, and numerical solvers tend to depend strongly on good initial values. In this work, we develop a new locally convergent algorithm with an explicit residual criterion that ensures convergence to the inverse problem solution, and a globalized variant that is guaranteed to automatically switch to the faster locally convergent algorithm after finitely many global search steps.
