Towards the resolution of the Gibbs phenomena
By Bernie D. Shizgal, Jae-Hun Jung. 2003
116 citations recorded by the source corpus.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/3159aa5fe86a8565b06524da368f3429827758bb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Bibek Dhital
- Marco Reisert
- Elias Kellner
- Jae-Hun Jung
- John P. Boyd
- Bernie D. Shizgal
- Jared Tanner
- Anne Gelb
In Statistical and Nonlinear Physics
Citations in the corpus
- Gibbs‐ringing artifact removal based on local subvoxel‐shifts (2015, methodology): “One reason for this might be that standard filtering approaches inevitably reduce the effective image resolution, and more advanced methods like Gegenbauer rereconstruction (4, 2, 8, 9) or data extrapolation methods (10, 11) are practically difficult to handle due to their complexity and, the requir”
- Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon (2004, methodology): “Only when N → ∞ is the matrix which represents the projection onto the Fourier space from the Gegenbauer space the inverse of the matrix which represents the projection onto the Gegenbauer space from the Fourier space [17].”
- Exponentially-Convergent Strategies for Defeating the Runge Phenomenon for the Approximation of Non-Periodic Functions, Part I: Single-Interval Schemes (2009, unknown): “• Tikhonov Regularization [2]; • Gegenbauer Regularization and its generalizations; [5, 6, 13–15, 17–24, 30, 34]; • Overdetermined Least-Squares [9]; • Mock-Chebyshev sub-sampling [9]; • Gaussian Radial Basis Functions, Slowly Flattening with N [8]; • Fourier Extension [4]; • Platte’s Undetermined L”
- Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations (2005, background): “The success of Gegenbauer reconstruction has spawned an industry of theoretical papers [21,16–19,12,9,10,23–25,32,26,11] and applications in fluid mechanics [29–31,7], hyperbolic waves [15], local Fourier methods [35,36] and medical imaging [2,1,3,14].”