Work

A local Fourier extension method for function approximation

Year: 2025

Type: article

Abstract: This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method achieves spectral accuracy at $ \mathcal{O}(M) $ computational complexity. Theoretical error bounds and parameter dependency analyses validate the robustness of the proposed method. The relationship among the key parameters involved is analytically established, accompanied by an optimized parameter selection strategy. Numerical experiments further confirm the effectiveness of the proposed method.

Source: Inverse Problems and Imaging

DOI: 10.3934/ipi.2025042

Authors: Zhenyu Zhao, Yanfei Wang

Institutions: Shandong University of Technology, Chinese Academy of Sciences, Institute of Geology and Geophysics

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Natural Science Foundation of China, Russian Science Foundation

Awards: G7187802179, G7247445720