A Fast Chebyshev Spectral Method for Nonlinear Fourier Transform

2019/09/09 by Vishal Vaibhav, Vaibhav, Vishal
Computer Science · Engineering · Physics and Astronomy · #Advanced Fiber Laser Technologies #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #Optical Network Technologies

paper · pdf · doi:10.48550/arxiv.1909.03710

openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of O(N_iter.Nlog N) per spectral node for N samples of the signal at the Chebyshev nodes where N_iter. is the number of iterations of the biconjugate gradient stabilized method.

Citations

• Is Gauss Quadrature Better than Clenshaw–Curtis?
• A Fast and Well-Conditioned Spectral Method

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