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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08 Dec 2014TL;DR: This paper proposes a robust method to solve the absolute rotation estimation problem, which arises in global registration of 3D point sets and in structure-from-motion, by casting the problem as a "low-rank & sparse" matrix decomposition.
Abstract: This paper proposes a robust method to solve the absolute rotation estimation problem, which arises in global registration of 3D point sets and in structure-from-motion. A novel cost function is formulated which inherently copes with outliers. In particular, the proposed algorithm handles both outlier and missing relative rotations, by casting the problem as a "low-rank a sparse" matrix decomposition. As a side effect, this solution can be seen as a valid and cost-effective detector of inconsistent pair wise rotations. Computational efficiency and numerical accuracy, are demonstrated by simulated and real experiments.
53 citations
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TL;DR: In this article, error bounds are derived for a first-order expansion of the LU factorization of a perturbation of the identity, and the results are applied to obtain perturbations expansions of LU, Cholesky, and QR factorizations.
Abstract: In this paper error bounds are derived for a first-order expansion of the LU factorization of a perturbation of the identity The results are applied to obtain perturbation expansions of the LU, Cholesky, and QR factorizations
53 citations
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TL;DR: This work proposes a multiscale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes and considers the inverse problem of decomposing the data matrix into its multiscales low rank components and approach the problem via a convex formulation.
Abstract: We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often exhibit local correlations in multiple scales. Concretely, we propose a multiscale low rank modeling that represents a data matrix as a sum of block-wise low rank matrices with increasing scales of block sizes. We then consider the inverse problem of decomposing the data matrix into its multiscale low rank components and approach the problem via a convex formulation. Theoretically, we show that under various incoherence conditions, the convex program recovers the multiscale low rank components either exactly or approximately. Practically, we provide guidance on selecting the regularization parameters and incorporate cycle spinning to reduce blocking artifacts. Experimentally, we show that the multiscale low rank decomposition provides a more intuitive decomposition than conventional low rank methods and demonstrate its effectiveness in four applications, including illumination normalization for face images, motion separation for surveillance videos, multiscale modeling of the dynamic contrast enhanced magnetic resonance imaging, and collaborative filtering exploiting age information.
53 citations
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TL;DR: A modified estimator based on the QR decomposition to combat the multicollinearity problem of design matrix is proposed in partially linear regression model which makes the data to be less distorted than the other methods.
53 citations
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TL;DR: This paper analytically establishes that the QRD-based design is indeed optimal for any performance measure under a SPC, and proposes an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework.
Abstract: We consider the beamformer design for multiple-input multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently.
53 citations