14,548 research outputs found
Ordered fast fourier transforms on a massively parallel hypercube multiprocessor
Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine
On the numerical calculation of the roots of special functions satisfying second order ordinary differential equations
We describe a method for calculating the roots of special functions
satisfying second order linear ordinary differential equations. It exploits the
recent observation that the solutions of a large class of such equations can be
represented via nonoscillatory phase functions, even in the high-frequency
regime. Our algorithm achieves near machine precision accuracy and the time
required to compute one root of a solution is independent of the frequency of
oscillations of that solution. Moreover, despite its great generality, our
approach is competitive with specialized, state-of-the-art methods for the
construction of Gaussian quadrature rules of large orders when it used in such
a capacity. The performance of the scheme is illustrated with several numerical
experiments and a Fortran implementation of our algorithm is available at the
author's website
A class of AM-QFT algorithms for power-of-two FFT
This paper proposes a class of power-of-two FFT (Fast Fourier Transform)
algorithms, called AM-QFT algorithms, that contains the improved QFT (Quick
Fourier Transform), an algorithm recently published, as a special case. The
main idea is to apply the Amplitude Modulation Double Sideband - Suppressed
Carrier (AM DSB-SC) to convert odd-indices signals into even-indices signals,
and to insert this elaboration into the improved QFT algorithm, substituting
the multiplication by secant function. The 8 variants of this class are
obtained by re-elaboration of the AM DSB-SC idea, and by means of duality. As a
result the 8 variants have both the same computational cost and the same memory
requirements than improved QFT. Differently, comparing this class of 8 variants
of AM-QFT algorithm with the split-radix 3add/3mul (one of the most performing
FFT approach appeared in the literature), we obtain the same number of
additions and multiplications, but employing half of the trigonometric
constants. This makes the proposed FFT algorithms interesting and useful for
fixed-point implementations. Some of these variants show advantages versus the
improved QFT. In fact one of this variant slightly enhances the numerical
accuracy of improved QFT, while other four variants use trigonometric constants
that are faster to compute in `on the fly' implementations
Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D
Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included
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