54,627 research outputs found
Shape Theory via QR decomposition
This work sets the non isotropic noncentral elliptical shape distributions
via QR decomposition in the context of zonal polynomials, avoiding the
invariant polynomials and the open problems for their computation. The new
shape distributions are easily computable and then the inference procedure can
be studied under exact densities instead under the published approximations and
asymptotic densities under isotropic models. An application in Biology is
studied under the classical gaussian approach and a two non gaussian models.Comment: 13 page
Improving Fixed-Point Implementation of QR Decomposition by Rounding-to-Nearest
QR decomposition is a key operation in many
current communication systems. This paper shows how to reduce
the area of a fixed-point QR decomposition implementation
based on Givens rotations by using a new number representation
system. This new representation allows performing round-tonearest
at the same cost of truncation. Consequently, the
rounding errors of the results are halved, which allows it to
reduce the word-length by one bit. This reduction positively
impacts on the area, delay and power consumption of the design.Ministry of Education and Science of Spain and Junta of Andalucía under contracts TIN2013-42253-P
and TIC-1692, respectively, and Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech
A low complexity multi-layered space frequency coding detection algorithm for MIMO-OFDM
A low complexity multi-layered space frequency OFDM (MLSF-OFDM) coding scheme is presented with the proposed two detection algorithms, fast QR decomposition detection algorithm or denoted as FAST-QR and enhanced FAST-QR (E-FAST-QR). Both algorithms not only reduce the implementation complexity of QR decomposition but also show a good performance in terms of bit error rate (BER). Hence, the proposed detection algorithms can be used to maintain guaranteed quality of service (QoS) in MIMO-OFDM system
GR decompositions and their relations to Cholesky-like factorizations
For a given matrix, we are interested in computing GR decompositions ,
where is an isometry with respect to given scalar products. The orthogonal
QR decomposition is the representative for the Euclidian scalar product. For a
signature matrix, a respective factorization is given as the hyperbolic QR
decomposition. Considering a skew-symmetric matrix leads to the symplectic QR
decomposition. The standard approach for computing GR decompositions is based
on the successive elimination of subdiagonal matrix entries. For the hyperbolic
and symplectic case, this approach does in general not lead to a satisfying
numerical accuracy. An alternative approach computes the QR decomposition via a
Cholesky factorization, but also has bad stability. It is improved by repeating
the procedure a second time. In the same way, the hyperbolic and the symplectic
QR decomposition are related to the and a skew-symmetric Cholesky-like
factorization. We show that methods exploiting this connection can provide
better numerical stability than elimination-based approaches
Direct QR factorizations for tall-and-skinny matrices in MapReduce architectures
The QR factorization and the SVD are two fundamental matrix decompositions
with applications throughout scientific computing and data analysis. For
matrices with many more rows than columns, so-called "tall-and-skinny
matrices," there is a numerically stable, efficient, communication-avoiding
algorithm for computing the QR factorization. It has been used in traditional
high performance computing and grid computing environments. For MapReduce
environments, existing methods to compute the QR decomposition use a
numerically unstable approach that relies on indirectly computing the Q factor.
In the best case, these methods require only two passes over the data. In this
paper, we describe how to compute a stable tall-and-skinny QR factorization on
a MapReduce architecture in only slightly more than 2 passes over the data. We
can compute the SVD with only a small change and no difference in performance.
We present a performance comparison between our new direct TSQR method, a
standard unstable implementation for MapReduce (Cholesky QR), and the classic
stable algorithm implemented for MapReduce (Householder QR). We find that our
new stable method has a large performance advantage over the Householder QR
method. This holds both in a theoretical performance model as well as in an
actual implementation
An algorithm for computing the QR decomposition of a polynomial matrix
This paper introduces an algorithm for computing a QR decomposition of a polynomial matrix. The algorithm proceeds to perform the decomposition by following the same strategy in eliminating entries of the matrix as is used in the Givens method for a QR decomposition of a scalar matrix. However scalar Givens rotation matrices can no longer be applied. Instead, a polynomial Givens rotation is introduced, enabling the QR decomposition of a polynomial matrix. Convergence of the algorithm is discussed and through simulations the capability of the algorithm is assessed
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