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A singular value decomposition updating algorithm for subspace tracking

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds.

These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing.

In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms.

His current research interests include Radar Signal Processing, Blind Source Separation and Broadband Wireless Communication Technology.

Jianqiang Qin received the Bachelor’s and Master’s degree from Xi’an Research Institute of High Technology, Xi’an, Shaanxi, China, in 20, respectively, both in electrical engineering.

Finally, numerical simulations and practical application are carried to further demonstrate the efficiency of the proposed algorithm.

Xiaowei Feng received the Bachelor’s and master’s degree from Xi’an Research Institute of High Tech-nology, Xi’an, China, in 20, respectively, both in electrical engineering.Moreover, convergence analysis shows that the proposed algorithm converges to a stationary point that relates to the principal singular values.Thus, compared with traditional algorithms who can only track the PSS, the proposed algorithm can not only track the PSS but also estimate all of the corresponding principal singular values based on the extracted subspace. In this paper, we extend the well known QR-updating scheme to a similar but more versatile and generally applicable scheme for updating the singular value decomposition (SVD).This is done by supplementing the QR-updating with a Jacobi-type SVD procedure, where apparently only a few SVD steps after each QR-update suffice in order to restore an acceptable approximation for the SVD.Since 1997, he has been with the Xi’an Research Institute of High Technology, Xi’an Shaanxi province, China. His research interests include adaptive signal processing, nonlinear system modeling and its application, and fault diagnosis.Donghui Xu received the Bachelor’s and Master’s degree from Xi’an Research Institute of High Technology, Xi’an, Shaanxi, China, in 20, respectively, both in Signal Processing.The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms.It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.It is a difficult problem because one must extract and interpret anomalous patterns from large amounts of ..." Anomalies are unusual and significant changes in a network's traffic levels, which can often span multiple links.Diagnosing anomalies is critical for both network operators and end users. Many algorithms have been proposed to deal with some but not all of these problems.

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