高阶数值导数的分数阶Landweber方法
A Fractional Landweber Method for Higher-Order Numerical Derivatives
摘要: 本文研究高阶数值微分问题，这是一个经典的不适定问题。首先对问题的不适定性进行分析并给出条件稳定性结果，之后通过分数阶Landweber迭代方法给出正则解，最后在正则化参数的先验选取规则下，得到正则解和精确解之间的误差估计。
Abstract: In the paper, we consider the higher-order numerical differentiation problem, which is a classical ill-posed problem. First, we discuss the ill-posed problem and provide the conditional stability results. Then, the regularized solution is obtained by the fractional Landweber iteration method. Finally, the error estimation of regularization solution and exact solution under the priori choice rules of the regularization parameter is generated.
文章引用：李刚刚. 高阶数值导数的分数阶Landweber方法[J]. 理论数学, 2024, 14(7): 61-68. https://doi.org/10.12677/pm.2024.147272

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