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In this letter, we present a fast and well-conditioned spectral method basedon the Chebyshev polynomials for computing the continuous part of the nonlinearFourier spectrum. The algorithm achieves a complexity of$O(N_{\text{iter.}}N\log N)$ per spectral node for $N$ samples of the signal atthe Chebyshev nodes where $N_{\text{iter.}}$ is the number of iterations of thebiconjugate gradient stabilized method.

A Fast Chebyshev Spectral Method for Nonlinear Fourier Transform