Numerical differentiation by a Fourier extension method with super-order regularization

作者：Chen, Baoqin; Zhao, Zhenyu^*; Li, Zhi; Meng, Zehong

来源：Applied Mathematics and Computation, 2018, 334: 1-10.

DOI：10.1016/j.amc.2018.04.005

• Numerical differentiation
• Fourier extension
• Tikhonov regularization method
• Supper-order regularization
• Discrepancy principle
• Ill posed problem

Based on the idea of Fourier extension, we develop a new method for numerical differentiation. The Tikhonov regularization method with a super-order penalty term is presented to deal with the illposdness of the problem and the regularization parameter can be chosen by a discrepancy principle. For various smooth conditions, the solution process of the new method is uniform and order optimal error bounds can be obtained. Numerical experiments are also presented to illustrate the effectiveness of the proposed method.

• 出版日期2018-10-1
• 单位广东海洋大学; 浙江财经大学