2023/12/13 by Haiyong Wang, Wang, Haiyong, Lun Zhang +1 · 1 citation
Mathematics · #41A05 #41A10 #41A25 #65D30 #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2312.07940
openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a rigorous analysis of root-exponential convergence of Hermite approximations, including projection and interpolation methods, for functions that are analytic in an infinite strip containing the real axis and satisfy certain restrictions on the asymptotic behavior at infinity within this strip. Asymptotically sharp error bounds in the weighted and maximum norms are derived. The key ingredients of our analysis are some remarkable contour integral representations for the Hermite coefficients and the remainder of Hermite spectral interpolations. Further extensions to Gauss--Hermite quadrature, Hermite spectral differentiations, generalized Hermite spectral approximations and the scaling factor of Hermite approximation are also discussed. Numerical experiments confirm our theoretical results.