An in-place truncated Fourier transform

The Truncated Fourier Transform andApplicationsJoris

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 jumpss 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 ...

An Illustrated Introduction to the Truncated Fourier Transform

The Truncated Fourier Transform (tft) is a variation of the Discrete Fourier Transform (dft/fft) that allows for input vectors that do not have length 2 n for n a positive integer. We present the univariate version of the tft, originally due to Joris van der Hoeven, heavily illustrating the presentation in order to make these methods accessible to a broader audience.

Notes on the Truncated Fourier Transform

In a previous paper [vdH04], we introduced 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, a non-trivial asymptotic factor was gained with...

An Improvement in Quantum Fourier Transform

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. In this work we introduce a new approach to improve the preciseness of the standard Quantum Fourier Transform. The presented Quantum-SVD algorithm is based on the singular value dec...

Discrete integer Fourier transform in real space: elliptic Fourier transform