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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 computation of the eigenvalues of a symmetric dpss matrix can be reduced by a congruence transformation to solving a generalized symmetric definite tridiagonal eigenproblem and a set of recurrence relations for evaluating the characteristic polynomial of a dpSS matrix in a stable way at a linear time is devised.
Abstract: In this paper we study both direct and inverse eigenvalue problems for diagonal-plus-semiseparable (dpss) matrices. In particular, we show that the computation of the eigenvalues of a symmetric dpss matrix can be reduced by a congruence transformation to solving a generalized symmetric definite tridiagonal eigenproblem. Using this reduction, we devise a set of recurrence relations for evaluating the characteristic polynomial of a dpss matrix in a stable way at a linear time. This in turn allows us to apply divide-and-conquer eigenvalue solvers based on functional iterations directly to dpss matrices without performing any preliminary reduction into a tridiagonal form. In the second part of the paper, we exploit the structural properties of dpss matrices to solve the inverse eigenvalue problem of reconstructing a symmetric dpss matrix from its spectrum and some other informations. Finally, applications of our results to the computation of a QR factorization of a Cauchy matrix with real nodes are provided.

20 citations

Journal ArticleDOI
TL;DR: This paper presents a fast CS reconstruction algorithm implemented on field-programmable gate array (FPGA) using OMP that adopts an incremental QR decomposition (QRD) method to efficiently solve the least square problem (LSP).
Abstract: Compressive sensing (CS) is a novel signal processing technology to reconstruct the sparse signal at sub-Nyquist rate. Orthogonal matching pursuit (OMP) is one of the most widely used signal reconstruction algorithms. However, the least square problem (LSP) in OMP algorithm limits its performance. This paper presents a fast CS reconstruction algorithm implemented on field-programmable gate array (FPGA) using OMP. The proposed algorithm adopts an incremental QR decomposition (QRD) method to efficiently solve the LSP. The incremental QRD is further optimized to eliminate the square root operation to facilitate hardware implementation. The proposed architecture avoiding the complex square root unit mainly consists of some more basic computing units, where the computing process is broken down into several simple operations to map to the corresponding hardware for pipelining. The proposed implementation based on Xilinx Kintex-7 FPGA exploits the parallelism by a well-planned workload schedule and reaches an optimal tradeoff between the latency and frequency. The experimental results demonstrate that the proposed architecture can run at a frequency of 210 MHz with a reconstruction time of 238 $\mu \text{s}$ for 36-sparse 1024-length signal, which improves the signal reconstruction speed by $1.43\times $ compared to the state-of-the-art implementations.

20 citations

Journal Article
TL;DR: It is demonstrated that, the proposed column oriented QR decomposition algorithm which uses MDA for column ordering and VPAIR for row ordering can lead to a much faster PSSE.

20 citations

Journal ArticleDOI
TL;DR: The basic theory of SVD will be presented, one simple example given for clarification, and a matrix representation of a sculptured head of Abe Lincoln will be used to illustrate the geometry involved.
Abstract: (1983). Visualization of Matrix Singular Value Decomposition. Mathematics Magazine: Vol. 56, No. 3, pp. 161-167.

20 citations

Journal ArticleDOI
TL;DR: This letter presents a predistortion algorithm which identifies the power amplifier (PA) model and accurately calculates thepredistortion function from the model by a new method which constructs a univariate polynomial and finds its roots by QR factorization.
Abstract: This letter presents a predistortion algorithm which identifies the power amplifier (PA) model and accurately calculates the predistortion function from the model by a new method. The method constructs a univariate polynomial and finds its roots by QR factorization. Although additional calculations are required, the new algorithm can compensate the nonlinearity of the PA more precisely and reduce the normalized mean square error (NMSE) performance of the new algorithm to the NMSE of the PA modeling. Simulation results demonstrate that the new algorithm outperforms the conventional algorithm by 4dB in the adjacent channel leakage ratio (ACLR) performance.

20 citations


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