Discrete weighted transforms and large-integer arithmetic
Mathematics of Computation
Topics in advanced scientific computation
Topics in advanced scientific computation
Modern Computer Algebra
The truncated fourier transform and applications
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Fast fourier transform algorithms with applications
Fast fourier transform algorithms with applications
An in-place truncated fourier transform and applications to polynomial multiplication
Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation
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Truncated Fourier Transforms (TFTs), first introduced by van der Hoeven, refer to a family of algorithms that attempt to smooth ``jumps'' in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in terms of ring operations, is asymptotically equivalent to existing not-in-place TFT methods. We also describe a transformation that maps between two families of TFT algorithms that use different sets of evaluation points.