A Bayesian Framework for Spectral Reprojection

Li, Tongtong; Gelb, Anne

doi:10.1007/s10915-025-02811-6

Title: A Bayesian Framework for Spectral Reprojection

Journal Article · 30 January 2025 · Journal of Scientific Computing

DOI: https://doi.org/10.1007/s10915-025-02811-6 · OSTI ID:2507483

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Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

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Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI ID:: 2507483

Journal Information:: Journal of Scientific Computing, Journal Name: Journal of Scientific Computing Journal Issue: 3 Vol. 102; ISSN 0885-7474

Publisher:: Springer Science + Business MediaCopyright Statement

Country of Publication:: United States

Language:: English

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