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math.NA2025
Fast numerical derivatives based on multi-interval Fourier extension
Zhenyu Zhao, Yanfei Wang, Xinran Liu
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval F…
math.NA2025
A Local Fourier Extension Method for Function Approximation
Zhenyu Zhao, Yanfei Wang
This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subre…
math.NA2025
Fourier Extension Based on Weighted Generalized Inverse
Zhenyu Zhao, Yanfei Wang, Anatoly G. Yagola +1
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high appr…