A numerical differentiation method based on legendre expansion with super order Tikhonov regularization

作者：

Highlights：

• We replace the penalty term in the Tikhonov functional with a new one.

• The order optimal error bounds can be obtained for various smooth conditions.

• The solution process of the new method is uniform for different smoothness conditions.

摘要

•We replace the penalty term in the Tikhonov functional with a new one.•The order optimal error bounds can be obtained for various smooth conditions.•The solution process of the new method is uniform for different smoothness conditions.

论文关键词：Numerical differentiation,Ill posed problem,Super order Tikhonov regularization,Legendre approximation,Discrepancy principle

论文评审过程：Received 18 February 2020, Revised 8 November 2020, Accepted 11 November 2020, Available online 21 November 2020, Version of Record 21 November 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125811