Efficient Nonlinear Fourier Transform algorithms of orderfFour on equispaced grid
Vishal Vaibhav (TU Delft - Team Raf Van de Plas)
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Abstract
We explore two classes of exponential integrators, in this letter, to design the nonlinear Fourier transform (NFT) algorithms with a convergence order of four on an equispaced grid. The integrating factor-based method in the class of the Runge-Kutta methods yields algorithms with complexity O(N\log2N) (where N is the number of samples of the signal), which have superior accuracy-complexity tradeoff than any of the fast methods known currently. The integrators based on Magnus series expansion, namely, standard and commutator-free Magnus methods yield the algorithms of complexity O(N2) that have superior error behavior than that of the fast methods.