Topic
QR decomposition
About: QR decomposition is a research topic. Over the lifetime, 3504 publications have been published within this topic receiving 100599 citations. The topic is also known as: QR factorization.
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TL;DR: This paper discusses a hybrid Monte Carlo and numerical integration EM algorithm for computing the maximum likelihood estimates for linear and nonlinear mixed models with censored data, and uses an efficient block-sampling scheme, automated monitoring of convergence, and dimension reduction based on the QR decomposition.
62 citations
TL;DR: The proposed ED-TAS algorithms are amalgamated with the low-complexity yet efficient power allocation (PA) technique, termed as TAS-PA, for the sake of further improving the system's performance.
Abstract: The benefits of transmit antenna selection (TAS) invoked for spatial modulation (SM) aided multiple-input multiple-output (MIMO) systems are investigated. Specifically, we commence with a brief review of the existing TAS algorithms and focus on the recently proposed Euclidean distance-based TAS (ED-TAS) schemes due to their high diversity gain. Then, a pair of novel ED-TAS algorithms, termed as the improved QR decomposition (QRD)-based TAS (QRD-TAS) and the error-vector magnitude-based TAS (EVM-TAS) are proposed, which exhibit an attractive system performance at low complexity. Moreover, the proposed ED-TAS algorithms are amalgamated with the low-complexity yet efficient power allocation (PA) technique, termed as TAS-PA, for the sake of further improving the system’s performance. Our simulation results show that the proposed TAS-PA algorithms achieve signal-to-noise ratio (SNR) gains of up to 9 dB over the conventional TAS algorithms and up to 6 dB over the TAS-PA algorithm designed for spatial multiplexing systems.
62 citations
08 Jun 2011
TL;DR: An implementation of the tall and skinny QR (TSQR) factorization in the MapReduce framework is presented, and computational results for nearly terabyte-sized datasets are provided.
Abstract: The QR factorization is one of the most important and useful matrix factorizations in scientific computing. A recent communication-avoiding version of the QR factorization trades flops for messages and is ideal for MapReduce, where computationally intensive processes operate locally on subsets of the data. We present an implementation of the tall and skinny QR (TSQR) factorization in the MapReduce framework, and we provide computational results for nearly terabyte-sized datasets. These tasks run in just a few minutes under a variety of parameter choices.
62 citations
TL;DR: In this article, the authors investigated the condition number appropriate to the componentwise backward error analysis of triangular systems and found that the conditioning of a triangular system depends on the right-hand side as well as the coefficient matrix.
Abstract: Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracy—higher than the traditional condition numbers for linear systems suggest. This phenomenon is investigated by use of condition numbers appropriate to the componentwise backward error analysis of triangular systems. Results of Wilkinson are unified and extended. Among the conclusions are that the conditioning of a triangular system depends on the right-hand side as well as the coefficient matrix; that use of pivoting in LU, QR, and Cholesky factorisations can greatly improve the conditioning of a resulting triangular system; and that a triangular matrix may be much more or less ill-conditioned than its transpose.
61 citations
TL;DR: In this article, the authors show that the greedy algorithm introduced in [1] and [5] to perform the parallel QR decomposition of a dense rectangular matrix of sizem×n is optimal.
Abstract: We show that the greedy algorithm introduced in [1] and [5] to perform the parallel QR decomposition of a dense rectangular matrix of sizem×n is optimal. Then we assume thatm/n2 tends to zero asm andn go to infinity, and prove that the complexity of such a decomposition is asymptotically2n, when an unlimited number of processors is available.
61 citations