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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: This paper combines the BD technique with a minimum mean square error vector precoding (MMSE-VP) for achieving further gain in performance with minimal computational overhead and shows that the proposed BD-MVP brings substantial performance gain over existing multiuser MIMO algorithms.
Abstract: Block diagonalization (BD) algorithm is a generalization of the channel inversion that converts multiuser multi-input multi-output (MIMO) broadcast channel into single-user MIMO channel without inter-user interference. In this paper, we combine the BD technique with a minimum mean square error vector precoding (MMSE-VP) for achieving further gain in performance with minimal computational overhead. Two key ingredients to make our approach effective are the QR decomposition based block diagonalization and joint optimization of transmitter and receiver parameters in the MMSE sense. In fact, by optimizing precoded signal vector and perturbation vector in the transmitter and receiver jointly, we pursue an optimal balance between the residual interference mitigation and the noise enhancement suppression. From the sum rate analysis as well as the bit error rate simulations (both uncoded and coded cases) in realistic multiuser MIMO downlink, we show that the proposed BD-MVP brings substantial performance gain over existing multiuser MIMO algorithms.

45 citations

Journal ArticleDOI
TL;DR: A pair of multichannel least-squares lattice filter algorithms is presented, each m-channel filter stage is numerically stable and computationally efficient, with a computational complexity of O(m/sup 2/).
Abstract: A pair of multichannel least-squares lattice filter algorithms is presented. Each m-channel filter stage is numerically stable and computationally efficient, with a computational complexity of O(m/sup 2/). Both algorithms are based on the recursive QR decomposition of the forward and backward error matrices in each filter stage. The first algorithm uses orthogonal Givens rotations to compute the QR decomposition. The second algorithm uses fast Givens rotations for greater efficiency. Simulation results are presented, as well as an example of the algorithms' application in the enhancement of magnetoencephalographic signals. >

44 citations

Journal ArticleDOI
TL;DR: A simple and fast computational algorithm based on the relationship between the Effective Independence and Modal Kinetic Energy method, and on a downdating algorithm of the QR decomposition for a reduced modal matrix for sensor placement is presented.

44 citations

Posted Content
TL;DR: L-CCA as mentioned in this paper is an iterative algorithm which can compute Canonical Correlation Analysis (CCA) fast on huge sparse datasets, and it is shown to outperform other fast CCA approximation schemes on two real datasets.
Abstract: Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow since it involves implementing QR decomposition or singular value decomposition of huge matrices. In this paper we introduce L-CCA, a iterative algorithm which can compute CCA fast on huge sparse datasets. Theory on both the asymptotic convergence and finite time accuracy of L-CCA are established. The experiments also show that L-CCA outperform other fast CCA approximation schemes on two real datasets.

44 citations

Journal ArticleDOI
TL;DR: An improvement of the Jacobi singular value decomposition algorithm is proposed in this article, where the matrix is first reduced to a triangular form and the row-cyclic strategy preserves the triangularity.
Abstract: An improvement of the Jacobi singular value decomposition algorithm is proposed The matrix is first reduced to a triangular form It is shown that the row-cyclic strategy preserves the triangularity Further improvements lie in the convergence properties It is shown that the method converges globally and a proof of the quadratic convergence is indicated as well The numerical experiments confirm these theoretical predictions Our method is about 2-3 times slower than the standard QR method but it almost reaches the latter if the matrix is diagonally dominant or of low rank

44 citations


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