Exclusive robustness of Gegenbauer method to truncated convolution errors

  title={Exclusive robustness of Gegenbauer method to truncated convolution errors},
  author={Ehsan Faghihifar and Mahmood Akbari},
  journal={J. Comput. Phys.},


NIST Handbook of Mathematical Functions
This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.
A Padé-based algorithm for overcoming the Gibbs phenomenon
The standard Fourier–Padé approximation, which is known to improve on the convergence of partial summation in the case of periodic, globally analytic functions, is here extended to functions with jumps to exhibit exponential convergence globally for piecewise analytic functions when the jump location(s) are known.
Fast estimation of propagation constants in crossed gratings
Fourier-based modal methods are among the most effective numerical tools for the accurate analysis of crossed gratings. However, leading to computationally expensive eigenvalue equations
Spectral Methods in the Presence of Discontinuities
Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients
With a system of polynomials that the user is essentially free to choose, one can restore exponential accuracy in n and root-exponential accuracy in m and generalizes a result proved recently for piecewise Legendre polynmials.
Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating.
  • K. Edee, J. Plumey
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2015
The modal method based on Gegenbauer polynomials (MMGE) is extended to the case of bidimensional binary gratings. A new concept of modified polynomials is introduced in order to take into account
A Stability Barrier for Reconstructions from Fourier Samples
It is proved that any stable method for resolving the Gibbs phenomenon can converge at best root-exponentially fast in $m$ and any method with faster convergence must also be unstable, and in particular, exponential convergence implies exponential ill-conditioning.
Efficient implementation of B-spline modal method for lamellar gratings.
  • G. Granet
  • Physics
    Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2014
The B-spline modal method as applied to lamellar gratings analysis is revisited, and a new implementation is presented that takes into account discontinuities by putting a spline with a degenerate knot on them.