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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
01 Apr 2003
TL;DR: Efficient parallel algorithms for computing all possible subset regression models are proposed based on the dropping columns method that generates a regression tree to provide an efficient load balancing which results in no inter-processor communication.
Abstract: Efficient parallel algorithms for computing all possible subset regression models are proposed. The algorithms are based on the dropping columns method that generates a regression tree. The properties of the tree are exploited in order to provide an efficient load balancing which results in no inter-processor communication. Theoretical measures of complexity suggest linear speedup. The parallel algorithms are extended to deal with the general linear and seemingly unrelated regression models. The case where new variables are added to the regression model is also considered. Experimental results on a shared memory machine are presented and analyzed.

40 citations

Journal ArticleDOI
TL;DR: In this article, a CVTVQR decomposition-based linear matrix equation model was proposed to solve the complex-valued time-varying linear equation (CVTV-LME) problem.
Abstract: The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.

40 citations

Journal ArticleDOI
TL;DR: This work presents FORTRAN subroutines that update the QR decomposition in a numerically stable manner when A is modified by a matrix of rank one, or when a row or a column is inserted or deleted.
Abstract: Let the matrix A E R”““, m 2 n, have a QR decomposition A = QR, where Q E R”“” has orthonormal columns, and R E R”“” is upper triangular. Assume that Q and R are explicitly known. We present FORTRAN subroutines that update the QR decomposition in a numerically stable manner when A is modified by a matrix of rank one, or when a row or a column is inserted or deleted. These subroutines are modifications of the Algol procedures in Daniel et al. [5]. We also present a subroutine that permutes the columns of A and updates the QR decomposition so that the elements in the lower right corner of R will generally be small if the columns of A are nearly linearly dependent. This subroutine is an implementation of the rank-revealing QR decomposition scheme recently proposed by Chan [3].

40 citations

Journal ArticleDOI
TL;DR: This paper presents a low-complexity generalized sphere decoding (GSD) approach by transforming the original underdetermined problem into the full-column-rank one so that standard SD can be directly applied on the transformed problem.
Abstract: For underdetermined linear systems, original sphere decoding (SD) algorithms fail due to zero diagonal elements in the upper-triangular matrix of the QR or Cholesky factorization of the underdetermined matrix. To solve this problem, this paper presents a low-complexity generalized sphere decoding (GSD) approach by transforming the original underdetermined problem into the full-column-rank one so that standard SD can be directly applied on the transformed problem. Since the introduced transformation maintains the dimension of the original problem for all M-QAM's, the proposed GSD approach provides significant reduction in complexity as compared to other GSD schemes, especially for M-QAM with large signaling constellation. Both performance and expected complexity are analyzed to provide the comprehensive relationships between the performance and complexity of the proposed GSD and its parameters. Illustrative simulation and analytical results are in good agreement in terms of both the performance and complexity and indicate that with the properly selected design parameters, the proposed GSD scheme can approach the optimum maximumlikelihood decoding (MLD) performance with low complexity for underdetermined linear communication systems including underdetermined MIMO systems, and the proposed expected complexity analysis can be used as reliable complexity estimation for practical implementation of the proposed algorithm and serve as reference for other GSD algorithms.

40 citations

Journal ArticleDOI
TL;DR: An algorithm for determining the triangular decomposition H R*DR of a Hankel matrix H using O(n') operations is derived and can be used to compute the three-term recurrence relation for orthogonal polynomials from a moment matrix.
Abstract: An algorithm for determining the triangular decomposition H R*DR of a Hankel matrix H using O(n') operations is derived. The derivation is based on the Lanczos algorithm and the relation between orthogonalization of vectors and the triangular decomposition of moment matrices. The algorithm can be used to compute the three-term recurrence relation for orthogonal polynomials from a moment matrix.

40 citations


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