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SIAMSC
2010
159views more  SIAMSC 2010»
13 years 3 months ago
The Fast Generalized Gauss Transform
The fast Gauss transform allows for the calculation of the sum of N Gaussians at M points in O(N + M) time. Here, we extend the algorithm to a wider class of kernels, motivated by ...
Marina Spivak, Shravan K. Veerapaneni, Leslie Gree...
CORR
2008
Springer
112views Education» more  CORR 2008»
13 years 8 months ago
The discrete Fourier transform: A canonical basis of eigenfunctions
We exhibit a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to defines a novel transform which we call ...
Shamgar Gurevich, Ronny Hadani, Nir A. Sochen
GECCO
2005
Springer
131views Optimization» more  GECCO 2005»
14 years 2 months ago
Evolution of a human-competitive quantum fourier transform algorithm using genetic programming
In this paper, we show how genetic programming (GP) can be used to evolve system-size-independent quantum algorithms, and present a human-competitive Quantum Fourier Transform (QF...
Paul Massey, John A. Clark, Susan Stepney
CORR
2007
Springer
194views Education» more  CORR 2007»
13 years 8 months ago
Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs
Abstract—This paper presents a systematic methodology to derive and classify fast algorithms for linear transforms. The approach is based on the algebraic signal processing theor...
Markus Püschel, José M. F. Moura
APPML
2010
112views more  APPML 2010»
13 years 8 months ago
Computing Fourier transforms and convolutions of Sn-1-invariant signals on Sn in time linear in n
Let Sn denote the symmetric group on {1, . . . , n} and Sn-1 the stabilizer subgroup of n. We derive algorithms for computing Fourier transforms of left and right Sn-1-invariant s...
Michael Clausen, Ramakrishna Kakarala