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arXiv · 1903.11702

Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid

Vishal Vaibhav
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Abstract

We explore two classes of exponential integrators in this letter to design nonlinear Fourier transform (NFT) algorithms with a desired accuracy-complexity trade-off and a convergence order of $4$ on an equispaced grid. The integrating factor based method in the class of Runge-Kutta methods yield algorithms with complexity $O(N\log^2N)$ (where $N$ is the number of samples of the signal) which have superior accuracy-complexity trade-off than any of the fast methods known currently. The integrators based on Magnus series expansion, namely, standard and commutator-free Magnus methods yield algorithms of complexity $O(N^2)$ that have superior error behavior even for moderately small step-sizes and higher signal strengths.

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Vishal Vaibhav. 2019-03-26. Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid. https://doi.org/10.1109/lpt.2019.2925052

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