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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.


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Journal ArticleDOI
TL;DR: The regularization method of Tikhonov-Phillips is used, and a new systolic array is proposed for the case when the matrix is banded, which implements a QR-decomposition by plane rotations.
Abstract: The application of systolic arrays to linear, discrete ill-posed problems is considered. The regularization method of Tikhonov-Phillips is used, and a new systolic array is proposed for the case when the matrix is banded. The array implements a QR-decomposition by plane rotations, and it consists of approximately ${{k^2 } / 2}$ processor elements, where k is the bandwidth of the matrix. The computation time for the QR-decomposition is $O(n)$ (n is the dimension of the problem). A generalization of the array is also mentioned. The reduction to banded form is briefly discussed.

16 citations

Journal ArticleDOI
TL;DR: This paper presents a new maximum likelihood detection- (MLD-) based signal detection method for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) multiplexed with frequency domain spreading and codemultiplexing by utilizing signal Orthogonalization based on QR decomposition of the product of the channel and spreading code matrices in the frequency domain.
Abstract: This paper presents a new maximum likelihood detection- (MLD-) based signal detection method for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) multiplexing with frequency domain spreading and code multiplexing The proposed MLD reduces the computational complexity by utilizing signal orthogonalization based on QR decomposition of the product of the channel and spreading code matrices in the frequency domain Simulation results show that when the spreading factor and number of code multiplexed symbols are 16, the proposed MLD reduces the average received signal energy per bit-to-noise spectrum density ratio (Eb/N0) for the average packet error rate (PER) of 10-2 by approximately 12 dB compared to the conventional minimum mean-squared error- (MMSE-) based filtering for 4-by-4 MIMO multiplexing (16QAM with the rate-3/4 Turbo code is assumed)

15 citations

Proceedings ArticleDOI
20 May 2012
TL;DR: More than one pivots are selected and zero-insertion processes of Givens-rotations are performed in parallel like tournament in order to increase the throughput, and the QR decomposition performance significantly increases compared to the triangular systolic array (TSA) approach.
Abstract: This paper presents a high-speed hardware architecture of an improved Givens rotation-based QR decomposition, named tournament-based complex Givens rotation (T-CGR). In the proposed approach, more than one pivots are selected and zero-insertion processes of Givens-rotations are performed in parallel like tournament in order to increase the throughput. As a result, the QR decomposition performance significantly increases compared to the triangular systolic array (TSA) approach. Moreover, the circuit area was reduced due to the smaller number of flip-flops for holding the computed results during the decomposition process. The proposed QR decomposition hardware was implemented using TSMC 0.25 um technology. The experimental results show that the proposed architecture achieves 73.00% speed-up over the TACR/TSA-based architecture for the 8 × 8 matrix decomposition.

15 citations

Journal ArticleDOI
TL;DR: A prototype parallel algorithm for approximating eigenvalues of a dense nonsymmetric matrix on a linear, synchronous processor array, employing n distributed-memory processors to deliver all eigen values in O ( n 2 ) time.

15 citations

Book ChapterDOI
01 Sep 1990
TL;DR: This paper presents an “adaptive blocking” methodology for determining in a systematic manner an optimal blocking strategy for a uniprocessor machine and shows that the resulting blocking strategy is as good as any fixed-width blocking strategy.
Abstract: On most high-performance architectures, data movement is slow compared to floating-point (in particular, vector) performance. On these architectures block algorithms have been successful for matrix computations. By considering a matrix as a collection of submatrices (the so-called blocks) one naturally arrives at algorithms that require little data movement. The optimal blocking strategy, however, depends on the computing environment and on the problem parameters. Current approaches use fixed-width blocking strategies that are not optimal. This paper presents an “adaptive blocking” methodology for determining in a systematic manner an optimal blocking strategy for a uniprocessor machine. We demonstrate this technique on a block QR factorization routine on a uniprocessor. After generating timing models for the high-level kernels of the algorithm we can formulate the optimal blocking strategy in a recurrence relation that we can solve inexpensively with a dynamic programming technique. Experiments on one processor of a CRAY-2 show that in fact the resulting blocking strategy is as good as any fixed-width blocking strategy. So while we do not know the optimum fixed-width blocking strategy unless we re-run the same problem several times, adaptive blocking provides optimum performance in the very first run.

15 citations


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