Fast Algorithms for Fourier extension based on boundary interval data

This paper present a new algorithm for the computation of Fourier extension based on boundary data, which can obtain a super-algebraic convergent Fourier approximation for non-periodic functions. The algorithm calculates the extension part through boundary data and connects it with the original function to form a periodic smooth function. By testing the key parameters involved, their impact on the algorithm is clarified and the optimization setting scheme of the parameters is proposed. Compared with FFT, the algorithm only needs to increase the computational complexity by a fixed small amount.