29 research outputs found
Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
We present algorithms for the discrete cosine transform (DCT) and discrete
sine transform (DST), of types II and III, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~ 2N log_2 N to ~ (17/9) N log_2 N for a power-of-two transform size N.
Furthermore, we show that a further N multiplications may be saved by a certain
rescaling of the inputs or outputs, generalizing a well-known technique for N=8
by Arai et al. These results are derived by considering the DCT to be a special
case of a DFT of length 4N, with certain symmetries, and then pruning redundant
operations from a recent improved fast Fourier transform algorithm (based on a
recursive rescaling of the conjugate-pair split radix algorithm). The improved
algorithms for DCT-III, DST-II, and DST-III follow immediately from the
improved count for the DCT-II.Comment: 9 page
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and
discrete sine transform (DST-IV), as well as for the modified discrete cosine
transform (MDCT) and its inverse, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact
count is strictly lowered for all N > 4. These results are derived by
considering the DCT to be a special case of a DFT of length 8N, with certain
symmetries, and then pruning redundant operations from a recent improved fast
Fourier transform algorithm (based on a recursive rescaling of the
conjugate-pair split radix algorithm). The improved algorithms for DST-IV and
MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page
BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
BerkeleyGW is a massively parallel computational package for electron
excited-state properties that is based on the many-body perturbation theory
employing the ab initio GW and GW plus Bethe-Salpeter equation methodology. It
can be used in conjunction with many density-functional theory codes for
ground-state properties, including PARATEC, PARSEC, Quantum ESPRESSO, OCTOPUS
and SIESTA. The package can be used to compute the electronic and optical
properties of a wide variety of material systems from bulk semiconductors and
metals to nanostructured materials and molecules. The package scales to
10,000's of CPUs and can be used to study systems containing up to 100's of
atoms
Proteomic analysis of tumor necrosis factor-α resistant human breast cancer cells reveals a MEK5/Erk5-mediated epithelial-mesenchymal transition phenotype
Internationalizing the Honors Experience: Initiatives to Globalize an Honors Program
Presented at the 2008 Annual Conference of the National Collegiate Honors Counci
A modified split-radix FFT with fewer arithmetic operations
Recent results by Van Buskirk et al. have broken the record set by Yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power-of-two discrete Fourier transform (DFT). Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6 % fewer operations than Yavne, matching the count achieved by Van Buskirk’s programgeneration framework. We also discuss the application of our algorithm to real-data and real-symmetric (discrete cosine) transforms, where we are again able to achieve lower arithmetic counts than previously published algorithms