标题： 一种局部傅里叶扩展函数逼近方法 显示英文标题

标题： A Local Fourier Extension Method for Function Approximation

摘要： 本文提出了一种新颖的局部化傅里叶延拓方法，用于通过区域分割来逼近非周期函数。通过对计算域进行子区域划分并采用统一的离散化尺度，该方法实现了谱精度且具有$\mathcal{O}(M)$计算复杂度。理论误差界和参数依赖性分析验证了所提出方法的鲁棒性。文中解析建立了关键参数之间的关系，并提出了优化的参数选择策略。数值实验进一步验证了所提出方法的有效性。 显示英文摘要

摘要： This paper presents a novel localized Fourier extension method for approximating non-periodic functions through domain segmentation. By subdividing the computational domain into subregions and employing uniform discretization scales, the method achieves spectral accuracy with $\mathcal{O}(M)$ 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 verify the effectiveness of the proposed method.