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.

Simple and Efficient Nonparametric Method for Estimating the Number of Signals Without Eigendecomposition

Abstract: Inspired by the computational simplicity and numerical stability of QR decomposition, a nonparametric method for estimating the number of signals without eigendecomposition (MENSE) is proposed for the coherent narrowband signals impinging on a uniform linear array (ULA). By exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging, the number of signals is revealed in the rank of the QR upper-trapezoidal factor of the autoproduct of a combined Hankel matrix formed from the cross correlations between some sensor data. Since the infection of additive noise is defused, signal detection capability is improved. A new detection criterion is then formulated in terms of the row elements of the QR upper-triangular factor when finite array data are available, and the number of signals is determined as a value of the running index for which this ratio criterion is maximized, where the QR decomposition with column pivoting is also used to improve detection performance. The statistical analysis clarifies that the MENSE detection criterion is asymptotically consistent. Furthermore, the proposed MENSE algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model. The effectiveness of the MENSE is verified through numerical examples, and the simulation results show that the MENSE is superior in detecting closely spaced signals with a small number of snapshots and/or at relatively low signal-to-noise ratio (SNR)

Triangular Systolic Array withReduced Latency for QR-decomposition ofComplex Matrices

Abstract: ThenovelCORDIC-based architecture ofthe these weights (combiner unit). Theimplementation ofthe Triangular Systolic ArrayforQRD oflarge sizecomplex combiner unitisrather straightforward. Opposed tothat, the matrices ispresented. Theproposed architecture relies onQRD implementation oftheweightcalculation unitisquite using athree angle complex rotation approach thatprovides challenging. As itcanbeseenfrom(1)and(2)themain significant reduction oflatency (systolic operation time) and computational problem fortheZFandMMSE algorithms is makestheQRDinsuchawaythat theupper triangular matrix R matrix inversion, whichshould bedoneforevery subcarrier (or hasoniy real diagonal elements.

Branch-and-Bound Algorithms for Computing the Best-Subset Regression Models

Abstract: An efficient branch-and-bound algorithm for computing the best-subset regression models is proposed. The algorithm avoids the computation of the whole regression tree that generates all possible subset models. It is formally shown that if the branch-and-bound test holds, then the current subtree together with its right-hand side subtrees are cut. This reduces significantly the computational burden of the proposed algorithm when compared to an existing leaps-and-bounds method which generates two trees. Specifically, the proposed algorithm, which is based on orthogonal transformations, outperforms by O(n3) the leaps-and-bounds strategy. The criteria used in identifying the best subsets are based on monotone functions of the residual sum of squares (RSS) such as R2, adjusted R2, mean square error of prediction, and Cp. Strategies and heuristics that improve the computational performance of the proposed algorithm are investigated. A computationally efficient heuristic version of the branch-and-bound strategy ...

Rule base reduction: some comments on the use of orthogonal transforms

Abstract: Comments on recent publications about the use of orthogonal transforms to order and select rules in a fuzzy rule base. The techniques are well-known from linear algebra, and we comment on their usefulness in fuzzy modeling. The application of rank-revealing methods based on singular value decomposition (SVD) to rule reduction gives rather conservative results. They are essentially subset selection methods, and we show that such methods do not produce an "importance ordering", contrary to what has been stated in the literature. The orthogonal least-squares (OLS) method, which evaluates the contribution of the rules to the output, is more attractive for systems modeling. However, it has been shown to sometimes assign high importance to rules that are correlated in the premise. This hampers the generalization capabilities of the resulting model. We discuss the performance of rank-revealing reduction methods and advocate the use of a less complex method based on the pivoted QR decomposition. Further, we show how detection of redundant rules can be introduced in OLS by a simple extension of the algorithm. The methods are applied to a problem known from the literature and compared to results reported by other researchers.

Deterministic Column-Based Matrix Decomposition

Abstract: In this paper, we propose a deterministic column-based matrix decomposition method. Conventional column-based matrix decomposition (CX) computes the columns by randomly sampling columns of the data matrix. Instead, the newly proposed method (termed as CX_D) selects columns in a deterministic manner, which well approximates singular value decomposition. The experimental results well demonstrate the power and the advantages of the proposed method upon three real-world data sets.