13,257 research outputs found
A Modified KZ Reduction Algorithm
The Korkine-Zolotareff (KZ) reduction has been used in communications and
cryptography. In this paper, we modify a very recent KZ reduction algorithm
proposed by Zhang et al., resulting in a new algorithm, which can be much
faster and more numerically reliable, especially when the basis matrix is ill
conditioned.Comment: has been accepted by IEEE ISIT 201
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
Light Pair Correction to Bhabha Scattering at Small Angle
This work deals with the computation of electron pair correction to small
angle Bhabha scattering, in order to contribute to the improvement of
luminometry precision at LEP/SLC below 0.1% theoretical accuracy. The exact QED
four-fermion matrix element for , including all
diagrams and mass terms, is computed and different Feynman graph topologies are
studied to quantify the error of approximate calculations present in the
literature. Several numerical results, obtained by a Monte Carlo program with
full matrix element, initial-state radiation via collinear structure functions,
and realistic event selections, are shown and critically compared with the
existing ones. The present calculation, together with recent progress in the
sector of purely photonic corrections, contributes to achieve a
total theoretical error in luminometry at the 0.05% level, close to the current
experimental precision and important in view of the final analysis of the
electroweak precision data.Comment: LaTeX2e, 28 pages, 8 figures include
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
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