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: The block diagonal Jacket matrix decomposition is proposed, which is able not only to extend the conventional block diagonal channel decomposition but also to achieve the MIMO broadcast channel capacity.
Abstract: The block diagonalization (BD) is a linear precoding technique for multi-user multi-input multi-output (MIMO) broadcast channels, which is able to completely eliminate the multi-user interference (MUI), but it is not computationally efficient. In this paper, we propose the block diagonal Jacket matrix decomposition, which is able not only to extend the conventional block diagonal channel decomposition but also to achieve the MIMO broadcast channel capacity. We also prove that the QR algorithm achieves the same sum rate as that of the conventional BD scheme. The complexity analysis shows that our proposal is more efficient than the conventional BD method in terms of the number of the required computation.
25 citations
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TL;DR: The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems.
Abstract: Motivated by the Cayley–Hamilton theorem, a novel adaptive procedure, called a Power Sparse Approximate Inverse (PSAI) procedure, is proposed that uses a different adaptive sparsity pattern selection approach to constructing a right preconditioner M for the large sparse linear system Ax=b. It determines the sparsity pattern of M dynamically and computes the n independent columns of M that is optimal in the Frobenius norm minimization, subject to the sparsity pattern of M . The PSAI procedure needs a matrix–vector product at each step and updates the solution of a small least squares problem cheaply. To control the sparsity of M and develop a practical PSAI algorithm, two dropping strategies are proposed. The PSAI algorithm can capture an effective approximate sparsity pattern of A−1 and compute a good sparse approximate inverse M efficiently. Numerical experiments are reported to verify the effectiveness of the PSAI algorithm. Numerical comparisons are made for the PSAI algorithm and the adaptive SPAI algorithm proposed by Grote and Huckle as well as for the PSAI algorithm and three static Sparse Approximate Inverse (SAI) algorithms. The results indicate that the PSAI algorithm is at least comparable to and can be much more effective than the adaptive SPAI algorithm and it often outperforms the static SAI algorithms very considerably and is more robust and practical than the static ones for general problems. Copyright q 2008 John Wiley & Sons, Ltd.
25 citations
01 Jan 2003
TL;DR: In this article, the null subspace of the data matrix is constructed using the generalized singular value decomposition (GSVD) technique, or the generalized eigenvalue decomposition(GEVD) of the respective correlation matrices.
Abstract: A novel approach for multi–microphone speech dereverberation is presented. The method is based on the construction of the null subspace of the data matrix in the presence of colored noise, using the generalized singular value decomposition (GSVD) technique, or the generalized eigenvalue decomposition (GEVD) of the respective correlation matrices. The special Silvester structure of the filtering matrix, related to this subspace, is exploited for deriving a total least squares (TLS) estimate for the acoustical transfer functions (ATFs). Other, less robust but computationally more efficient methods are derived based on the same structure and on the QR decomposition (QRD). A preliminary study of the incorporation of the subspace method into a This research work was partly carried out at the ESAT laboratory of the Katholieke Universiteit Leuven, in the frame of the Interuniversity Attraction Pole IUAP P4-02, Modeling, Identification, Simulation and Control of Complex Systems, the Concerted Research Action Mathematical Engineering Techniques for Information and Communication Systems (GOA-MEFISTO-666) of the Flemish Government and the IT-project Multi-microphone Signal Enhancement Techniques for handsfree telephony and voice controlled systems (MUSETTE-2) of the I.W.T., and was partially sponsored by Philips-ITCL.
25 citations
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TL;DR: A weighted greedy QR decomposition (GQRD) is proposed to choose significant source points by introducing a weighting parameter and it is concluded that the numerical solution tends to be more accurate when the average degree of approximation is larger and that the proposed method can yield more accurate solutions with a less number of source points than the conventional GQRD.
25 citations
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07 Jun 2009TL;DR: Unified hardware architecture for fast, area efficient QR factorization based on the Householder transformation is presented and the design and implementation of the proposed hardware is presented with synthesis results based on FPGA hardware.
Abstract: The QR factorization is used in many signal processing and communication applications such as echo cancellation, adaptive beamforming and multiple-inputmultiple- output (MIMO) systems. However, division, square root and inverse square root operations required by the QR algorithm are very difficult to implement because they are computationally slow and area-consuming arithmetic operations. This paper presents unified hardware architecture for fast, area efficient QR factorization based on the Householder transformation. Newton-Raphson, and Goldschmidt algorithms are used for fast division, square root and inverse square root blocks. By using a unified architecture, area and power requirements for QR factorization are reduced without decreasing overall speed. The design and implementation of the proposed hardware is presented with synthesis results based on FPGA hardware.
25 citations