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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
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Journal ArticleDOI
TL;DR: The convergence, to the least-square solution y = A'x, is established, for the sequential two-stage iterative method and for the parallel stationary iterative methods.

20 citations

Journal ArticleDOI
01 Jul 2014
TL;DR: This work investigates the viability of implementing QR updating algorithms on GPUs and demonstrates that GPU-based updating for removing columns achieves speed-ups of up to 13.5x compared with full GPU QR factorization.
Abstract: Linear least squares problems are commonly solved by QR factorization. When multiple solutions need to be computed with only minor changes in the underlying data, knowledge of the difference between the old data set and the new can be used to update an existing factorization at reduced computational cost. We investigate the viability of implementing QR updating algorithms on GPUs and demonstrate that GPU-based updating for removing columns achieves speed-ups of up to 13.5x compared with full GPU QR factorization. We characterize the conditions under which other types of updates also achieve speed-ups.

20 citations

Journal ArticleDOI
TL;DR: A novel hierarchical approach for pipelining and folding the large CORDIC-based systolic array of a QR decomposition-based recursive least square algorithm (QRD-RLS) adaptive filter to a small fixed size array is presented.
Abstract: This paper presents a novel hierarchical approach for pipelining and folding the large CORDIC-based systolic array of a QR decomposition-based recursive least square algorithm (QRD-RLS) adaptive filter to a small fixed size array. With the annihilation-reordering look-ahead transformation, the iteration bound of a QRD-RLS adaptive filter can be reduced linearly with respect to the look-ahead factor. This paper presents, for the first time, how to pipeline and fold such a look-ahead transformed QRD-RLS adaptive filter. Unlike the previously published algorithms, this approach has low complexity and can result in a physical array of any size. In addition, a mathematical model for evaluating these transformations is developed. Using this model, it is shown how a combination of look-ahead, pipelining, and folding transformations can lead to a large increase in throughput and large reduction in area or power consumption. Therefore, the proposed approach is of great significance for application-specific IC chip design, high-level hardware synthesis, and special-purpose processor design. The optimally designed QRD-RLS adaptive filters can be used for adaptive digital beamforming applications, which play an important role in radar, sonar, and mobile/wireless communication systems.

20 citations

Journal ArticleDOI
TL;DR: In this article, a two-step procedure based on QR decompositions is proposed as a solution algorithm for this type of identification problem, which will always deliver the exact solution and is much easier to implement than a Newton-type iteration algorithm.

20 citations

Proceedings ArticleDOI
15 Dec 2010
TL;DR: The results show that very coarse approximations are sufficient for a reasonable positioning accuracy and the presented method reduces the computational complexity significantly and is highly suitable for hardware implementation.
Abstract: The efficient implementation of positioning algorithms is investigated for Global Positioning System (GPS) and Differential GPS (DGPS). This is particularly important for smart phones with battery limitations. With the help of the information from base stations, Assisted GPS (AGPS) and DGPS can do the positioning more efficiently and more precisely than GPS. In order to do the positioning, the pseudoranges between the receiver and the satellites are required. The most commonly used algorithm for position computation from pseudoranges is non-linear Least Squares (LS) method. Linearization is done to convert the non-linear system of equations into an iterative procedure, which requires the solution of a linear system of equations in each iteration, i.e. linear LS method is applied iteratively. CORDIC-based approximate rotations are used while computing the QR decomposition for solving the LS problem in each iteration. By choosing accuracy of the approximation, e.g. with a chosen number of optimal CORDIC angles per rotation, the LS computation can be simplified. The accuracy of the positioning results is compared for various numbers of required iterations and various approximation accuracies using real GPS data. The results show that very coarse approximations are sufficient for a reasonable positioning accuracy. Therefore, the presented method reduces the computational complexity significantly and is highly suitable for hardware implementation.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202331
202273
202190
2020132
2019126
2018139