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.

On the weighting method for mixed least squares–total least squares problems

Abstract: Summary It is well known that the standard algorithm for the mixed least squares–total least squares (MTLS) problem uses the QR factorization to reduce the original problem into a standard total least squares problem with smaller size, which can be solved based on the singular value decomposition (SVD). In this paper, the MTLS problem is proven to be closely related to a weighted total least squares problem with its error-free columns multiplied by a large weighting factor. A criterion for choosing the weighting factor is given; and for the sake of stability in solving the MTLS problem, the Cholesky factorization-based inverse (Cho-INV) iteration and Rayleigh quotient iteration are also considered. For large-scale MTLS problems, numerical tests show that Cho-INV is superior to the standard QR-SVD method, especially for the case with big gap between the desired and undesired singular values and the case when the coefficient matrix has much more error-contaminated columns. Rayleigh quotient iteration behaves more efficient than QR-SVD for most cases and fails occasionally, and in some cases, it converges much faster than Cho-INV but still less efficient due to its higher computation cost.

Dimensionality reduction for text-independent speaker identification using Gaussian mixture model

Abstract: Reducing the dimensionality of the training and testing data is crucial for text-independent speaker identification tasks. In this paper, the performance of various dimensionality reduction techniques is evaluated for speaker identification systems using Gaussian mixture model (GMM) as the statistical classifier. An enhancement of the standard linear discriminant analysis (LDA) is proposed in which class distributions are assumed to follow Gaussian mixture distribution. This assumption is more appropriate for asymmetric and multimodal class conditional densities. In addition, a new feature selection technique based on the QR factorization method is introduced. Computer simulation results reveal that the proposed modification to the LDA outperforms the standard algorithm in terms of classification accuracy. Moreover, the QR-based selection technique produces comparable results to other prominent dimensionality reduction techniques

Dynamical system analyser

Abstract: A dynamical system analyser (10) incorporates a computer (22) to perform a singular value decomposition of a time series of signals from a nonlinear (possibly chaotic) dynamical system (14). Relatively low-noise singular vectors from the decomposition are loaded into a finite impulse response filter (34). The time series is formed into Takens' vectors each of which is projected onto each of the singular vectors by the filter (34). Each Takens' vector thereby provides the co-ordinates of a respective point on a trajectory of the system (14) in a phase space. A heuristic processor (44) is used to transform delayed co-ordinates by QR decomposition and least squares fitting so that they are fitted to non-delayed co-ordinates. The heuristic processor (44) generates a mathematical model to implement this transformation, which predicts future system states on the basis of respective current states. A trial system is employed to generate like co-ordinates for transforation in the heuristic processor (44). This produces estimates of the trial system's future states predicted from the comparison system's model. Alternatively, divergences between such estimates and actual behavior may be obtained. As a further alternative, mathematical models derived by the analyser (10) from different dynamical systems may be compared.

Efficiency and scalability of two parallel QR factorization algorithms

Abstract: Both the Householder QR factorization algorithm and the modified Gram-Schmidt algorithm can be written in terms of matrix-matrix operations using the Compact WY representation. Parallelizations of the resulting algorithms are reviewed and analyzed. For this purpose a general framework for analyzing the scalability of parallel algorithms is presented. >