1. Block-row Hankel weighted low rank approximation. Author Schuermans, M., Lemmerling, P., and Van Huffel, S. Subjects APPROXIMATION theory, HANKEL functions, MATRICES (Mathematics), MATHEMATICAL optimization, ALGORITHMS Abstract This paper extends the weighted low rank approximation (WLRA) approach to linearly structured matrices. In the case of Hankel matrices with a special block structure, an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2006 Full Text View/download PDF
2. Symmetric low-rank corrections to quadratic models. Author Qian, Jiang, Xu, Shu-Fang, and Bai, Feng-Shan Subjects MATHEMATICAL symmetry, MATHEMATICAL models, ALGORITHMS, APPROXIMATION theory, NUMERICAL analysis, PROBLEM solving, MATHEMATICAL optimization Abstract In this paper, we study the quadratic model updating problems by using symmetric low-rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low-rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2009 Full Text View/download PDF
3. Structured weighted low rank approximation. Author Schuermans, M., Lemmerling, P., and Van Huffel, S. Subjects APPROXIMATION theory, HANKEL functions, MATRICES (Mathematics), MATHEMATICAL optimization, ALGORITHMS Abstract This paper extends the weighted low rank approximation (WLRA) approach towards linearly structured matrices. In the case of Hankel matrices an equivalent unconstrained optimization problem is derived and an algorithm for solving it is proposed. The correctness of the latter algorithm is verified on a benchmark problem. Finally the statistical accuracy and numerical efficiency of the proposed algorithm is compared with that of STLNB, a previously proposed algorithm for solving Hankel WLRA problems. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR] Published 2004 Full Text View/download PDF