数学杂志2026，Vol.46Issue(3)：165-176,12.
线性反问题的Crank-Nicolson正则化方法
CRANK-NICOLSON REGULARIZATION METHOD FOR LINEAR INVERSE PROBLEMS
摘要
Abstract
This paper investigates the Crank-Nicolson regularization method for linear inverse problems.By discretizing the continuous regularization equation with the Crank-Nicolson scheme,the method is proven to be a valid regularization strategy achieving optimal convergence order.Theoretical analysis shows that,under fixed step size,it shares similar regularization properties with the Landweber method.Under variable step sizes,its convergence condition is stricter than that of the nonstationary Tikhonov method,and geometric step sequences cannot achieve logarithmic iteration order.Numerical experiments confirm its regularization effectiveness and optimal error rate,while revealing the restriction with respect to the nonstationary Tikhonov method under low-noise conditions.关键词
线性反问题/连续正则化/Crank-Nicolson格式Key words
linear inverse problems/continuous regularization/Crank-Nicolson scheme分类
数理科学引用本文复制引用
高健铭,吕锡亮..线性反问题的Crank-Nicolson正则化方法[J].数学杂志,2026,46(3):165-176,12.基金项目
国家自然科学基金资助(12561160122) （12561160122）
湖北省自然科学基金资助(2024AFE006). （2024AFE006）
