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.
Papers published on a yearly basis
Papers
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TL;DR: This paper presents a direct and thorough comparison of many k-fold cross- validation versions as well as leave-one-out cross-validation versions, and demonstrates theoretically and experimentally that while the type of matrix decomposition plays one important role, another equally important role is played by the version of cross- validation.
28 citations
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TL;DR: Simulation results confirm the bit-error-rate (BER) and throughput performance superiority of the proposed systems compared to conventional SVD per-carrier precoding schemes.
Abstract: QR decomposition (QRD)-based precoded MIMO-OFDM systems with reduced feedback are proposed to convert the MIMO-OFDM channel into layered subchannels. QRD-M is further combined with either singular value (SVD) or geometric mean decomposition (GMD) of the time-domain channel impulse response matrix. As a result, the receiver in the proposed systems only needs to feed back information describing one precoding matrix for all carriers. Simulation results confirm the bit-error-rate (BER) and throughput performance superiority of the proposed systems compared to conventional SVD per-carrier precoding schemes.
28 citations
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TL;DR: The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing and the BSP complexity of Gaussian elimination and related problems is studied.
Abstract: The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We study the BSP complexity of Gaussian elimination and related problems. First, we analyze the Gaussian elimination without pivoting, which can be applied to the LU decomposition of symmetric positive-definite or diagonally dominant real matrices. Then we analyze the Gaussian elimination with Schonhage's recursive local pivoting suitable for the LU decomposition of matrices over a finite field, and for the QR decomposition of real matrices by the Givens rotations. Both versions of Gaussian elimination can be performed with an optimal amount of local computation, but optimal communication and synchronization costs cannot be achieved simultaneously. The algorithms presented in the paper allow one to trade off communication and synchronization costs in a certain range, achieving optimal or near-optimal cost values at the extremes. Bibliography: 19 titles.
28 citations
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TL;DR: This work considers a different so-called rank-revealing two-sided orthogonal decomposition which decomposes the matrix into a product of a unitARY matrix, a triangular matrix and another unitary matrix in such a way that the effective rank of the matrix is obvious and at the same time the noise subspace is exhibited explicity.
Abstract: Solving Total Least Squares (TLS) problemsAX≈B requires the computation of the noise subspace of the data matrix [A;B]. The widely used tool for doing this is the Singular Value Decomposition (SVD). However, the SVD has the drawback that it is computationally expensive. Therefore, we consider here a different so-called rank-revealing two-sided orthogonal decomposition which decomposes the matrix into a product of a unitary matrix, a triangular matrix and another unitary matrix in such a way that the effective rank of the matrix is obvious and at the same time the noise subspace is exhibited explicity. We show how this decompsition leads to an efficient and reliable TLS algorithm that can be parallelized in an efficient way.
28 citations
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06 Apr 1987TL;DR: A more computationally efficient solution to the QR RLS problem that requires only O(N) computations per time update, when the input has the usual shift-invariant property, and the computation and implementation requirements are reduced by an order of magnitude.
Abstract: There has been considerable recent interest in QR factorization for recursive solution to the least-squares adaptive-filtering problem, mainly because of the good numerical properties of QR factorizations. Early work by Gentleman and Kung (1981) and McWhirter (1983) has produced triangular systolic arrays of N2/2 processors that solve the Recursive Least Squares (RLS) adaptive-filtering problem (where N is the size of the adaptive filter). Here, we introduce a more computationally efficient solution to the QR RLS problem that requires only O(N) computations per time update, when the input has the usual shift-invariant property. Thus, computation and implementation requirements are reduced by an order of magnitude. The new algorithms are based on a structure that is neither a transversal filter nor a lattice, but can be best characterized by a functionally equivalent set of parameters that represent the time-varying "least-squares frequency transforms" of the input sequences. Numerical stability can be insured by implementing computations as 2 × 2 orthogonal (Givens) rotations.
28 citations