The truncated fourier transform and applications

In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the “jumps” in the complexity at powers of two. When applied to the multiplication of multivariate polynomials or truncated multivariate power series, we gain a logarithmic factor with respect to the best previously known algorithms. Categories and Subject Descriptors F.2.1 [Theory of Computation]: Analysis of algorithms and problem complexity—Numerical algorithms and problems General Terms Algorithms Keywords Fast Fourier Transform, jump phenomenon, truncated multiplication, FFT-multiplication, multivariate polynomials, multivariate power series.

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Joris van der Hoeven
• Keywords: Fast Fourier Transform, ISSAC 2004, Multivariate Polynomials, Multivariate Power Series