scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: A new algorithm for accurate downdating of least squares solutions is described and compared to existing algorithms and numerical test results are presented using the sliding window method.
Abstract: Solutions to a sequence of modified least squares problems, where either a new observation is added (updating) or an old observation is deleted (downdating), are required in many applications. Stable algorithms for downdating can be constructed if the complete QR factorization of the data matrix is available. Algorithms that only downdate $R$ and do not store $Q$ require less operations. However, they do not give good accuracy and may not recover accuracy after an ill-conditioned problem has occurred. The authors describe a new algorithm for accurate downdating of least squares solutions and compare it to existing algorithms. Numerical test results are also presented using the sliding window method, where a number of updatings and downdatings occur repeatedly.

53 citations

Proceedings ArticleDOI
13 Feb 2008
TL;DR: This paper examines the scalable parallel implementation of the QR factorization of a general matrix, targeting SMP and multi-core architectures, and shows that the implementation effort is greatly simplified by expressing the algorithms in code with the FLAME/FLASH API, which allows matrices stored by blocks to be viewed and managed as matrices of matrix blocks.
Abstract: This paper examines the scalable parallel implementation of the QR factorization of a general matrix, targeting SMP and multi-core architectures. Two implementations of algorithms-by-blocks are presented. Each implementation views a block of a matrix as the fundamental unit of data, and likewise, operations over these blocks as the primary unit of computation. The first is a conventional blocked algorithm similar to those included in libFLAME and LAPACK but expressed in a way that allows operations in the so-called critical path of execution to be computed as soon as their dependencies are satisfied. The second algorithm captures a higher degree of parallelism with an approach based on Givens rotations while preserving the performance benefits of algorithms based on blocked Householder transformations. We show that the implementation effort is greatly simplified by expressing the algorithms in code with the FLAME/FLASH API, which allows matrices stored by blocks to be viewed and managed as matrices of matrix blocks. The SuperMatrix run-time system utilizes FLASH to assemble and represent matrices but also provides out-of-order scheduling of operations that is transparent to the programmer. Scalability of the solution is demonstrated on ccNUMA platform with 16 processors and an SMP architecture with 16 cores.

53 citations

Journal ArticleDOI
TL;DR: The HSS algorithms are used to solve the dense Schur complement systems associated with the root separator of the separator tree obtained from nested dissection of the graph of discretized Helmholtz equations and iteratively solve time-harmonic seismic inverse boundary value problems.
Abstract: Hierarchically semiseparable (HSS) matrix techniques are emerging in constructing superfast direct solvers for both dense and sparse linear systems. Here, we develop a set of novel parallel algorithms for key HSS operations that are used for solving large linear systems. These are parallel rank-revealing QR factorization, HSS constructions with hierarchical compression, ULV HSS factorization, and HSS solutions. The HSS tree-based parallelism is fully exploited at the coarse level. The \textttBLACS and \textttScaLAPACK libraries are used to facilitate the parallel dense kernel operations at the fine-grained level. We appply our new solvers for discretized Helmholtz equations for multifrequency seismic imaging and iteratively solve time-harmonic seismic inverse boundary value problems. In particular, we use the HSS algorithms to solve the dense Schur complement systems associated with the root separator of the separator tree obtained from nested dissection of the graph of discretized Helmholtz equations. We...

53 citations

Journal ArticleDOI
01 Nov 1990
TL;DR: Proposed parallel algorithms for the modified Gram-Schmidt and the Householder algorithms on message passing systems in which the matrix is distributed by blocks or rows are studied.
Abstract: In this paper, the parallel implementation of two algorithms for forming a QR factorization of a matrix is studied. We propose parallel algorithms for the modified Gram-Schmidt and the Householder algorithms on message passing systems in which the matrix is distributed by blocks or rows. The models that predict performance of the algorithms are validated by experimental results on several parallel machines.

53 citations

Patent
26 Nov 2008
TL;DR: In this article, a closed loop MIMO communication utilizing implicit or explicit channel state information (CSI) at the transmitter and the receiver is described, where the receiver mitigates the mutual interference between the streams by performing MMSE processing on the received signals, and the MMSE matrix is computed with respect to the processed channel that may estimated by the receiver through preprocessed pilot signals.
Abstract: The present invention describes a method of closed loop MIMO communication utilizing implicit or explicit channel state information (CSI) at the transmitter and the receiver. The transmitter performs linear pre-processing (for example, QR decomposition or bi-diagonal decomposition or Jacobi rotations, and/or sporadic SVDs) on a channel matrix, and the receiver mitigates the mutual interference between the streams by performing MMSE processing on the received signals. The MMSE matrix is computed with respect to the processed channel that may estimated by the receiver through preprocessed pilot signals. The transmitters preprocessing is of much lesser cost and complexity than full SVD.

53 citations


Network Information
Related Topics (5)
Optimization problem
96.4K papers, 2.1M citations
85% related
Network packet
159.7K papers, 2.2M citations
84% related
Robustness (computer science)
94.7K papers, 1.6M citations
83% related
Wireless network
122.5K papers, 2.1M citations
83% related
Wireless sensor network
142K papers, 2.4M citations
82% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202331
202273
202190
2020132
2019126
2018139