Topic
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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TL;DR: These algorithms are based on earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.
Abstract: We present algorithms to determine the number of nonzeros in each row and column of the factors of a sparse matrix, for both the QR factorization and the LU factorization with partial pivoting. The algorithms use only the nonzero structure of the input matrix, and run in time nearly linear in the number of nonzeros in that matrix. They may be used to set up data structures or schedule parallel operations in advance of the numerical factorization. The row and column counts we compute are upper bounds on the actual counts. If the input matrix is strong Hall and there is no coincidental numerical cancellation, the counts are exact for QR factorization and are the tightest bounds possible for LU factorization. These algorithms are based on our earlier work on computing row and column counts for sparse Cholesky factorization, plus an efficient method to compute the column elimination tree of a sparse matrix without explicitly forming the product of the matrix and its transpose.
17 citations
TL;DR: The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one and the SAP preconditioner applied to the domain-decomposed lattice helps to minimize communication overhead.
17 citations
TL;DR: An experimental comparison of several numerical tools for computing the numerical rank of dense matrices and block-partitioned algorithms for the URV decomposition and rank-revealing QR factorizations which provide efficient implementations on shared memory environments are presented.
17 citations
13 May 2002
TL;DR: It is shown that for the optimal precoded channel, the detection performance using the decision feedback equalizer (DFE) based on QR decomposition is asymptotically equivalent to that of the mamximum likehood detector (MLD) when the signal to noise ratio (SNR) is large.
Abstract: Redundancy introduced using filterbank precoders at the transmitter builds a unified framework for modulation schems. Taking advantage of this diversity can offer a powerful tool for removing interblock interference and devising simple but effective precoders for suppressing the intersymbol interference (ISI) and being robust to frequency selective channels‥ In this paper, we assume that the transmitter knows the autocorrelation sequences of the channel impulse response. Under this assumption, we derive a lower and an upper bound on the free distance for a precoded channel and with this, design the precoder that maximizes the lower bound subject to a power constraint. It turns out that the optimal precoder is a unitary matrix which makes QR decomposition of its super-channel exhibit equal diagonal entries in R-factor and the lower and the upper bounds of its free distance equal. We show that for the optimal precoded channel, the detection performance using the decision feedback equalizer (DFE) based on QR decomposition is asymptotically equivalent to that of the mamximum likehood detector (MLD) when the signal to noise ratio (SNR) is large.
17 citations
TL;DR: In this paper, the structure of generalizations of the singular value decomposition and the QR decomposition for any number of matrices is analyzed as a function of the ranks of the matrices or their products and concatenations.
Abstract: This paper analyzes in detail the structure of generalizations of the singular value decomposition and the QR decomposition for any number of matrices. The structure is completely determined as a function of the ranks of the matrices or their products and concatenations.
17 citations