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The extremal solution of the matrix equation Xs + A*X-qA = I

APPLIED MATHEMATICS AND COMPUTATION 2013年 220卷 193-199页

作者： Wang, Minghui Wei, Musheng Hu, Shanrui Qingdao Univ Sci & Technol Dept Math Qingdao 266061 Peoples R China Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China

In this paper, the distribution of the positive definite solution of the nonlinear equation X-s + A*X(-q)A = I is deduced, the existence of the maximal solution and the minimal solution is discussed and two new iterative algorithms for obtaining these solutions are proposed. These algorithms avoid matrix inversion. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Positive definite matrix Nonlinear matrix equation iterative algorithm The maximal solution The minimal solution

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Decomposition based fast least squares algorithm for output error systems

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SIGNAL PROCESSING 2013年第5期93卷 1235-1242页

作者： Ding, Feng Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Control Sci & Engn Res Ctr Wuxi 214122 Peoples R China

Parameter estimation methods have wide applications in signal processing, communication and system identification. This paper derives an iterative least squares algorithm to estimate the parameters of output error systems and uses the partitioned matrix inversion lemma to implement the proposed algorithm in order to enhance computational efficiencies. The simulation results show that the proposed algorithm works well. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Signal processing Filtering Parameter estimation Fast least squares iterative algorithm

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The existence of solutions for systems of generalized set-valued nonlinear quasi-variational inequalities

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FIXED POINT THEORY AND APPLICATIONS 2013年第1期2013卷 1-15页

作者： Qiu, Y. Q. Li, X. L. Jiangxi Univ Sci & Technol Coll Appl Sci Ganzhou 341000 Jiangxi Peoples R China Nanchang Inst Technol Dept Sci Nanchang 330099 Peoples R China

In this paper, we introduce and study a class of new systems of generalized set-valued nonlinear quasi-variational inequalities in a Hilbert space. By using the projection operator technique and the system of Wiener-Hopf equations technique, we suggest several new iterative algorithms to find the approximate solutions to these problems and prove the convergence of the different types of iterative sequences respectively. It is the first time that the system of Wiener-Hopf equations technique has been used to solve the system of variational inequalities problems, and the technique is more general than the projection operator technique. Our results improve and extend some known results in the literature.

关键词： system of generalized set-valued nonlinear quasi-variational inequalities projection operator technique system of Wiener-Hopf equations iterative algorithm convergence criteria

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Two-dimensional contact mechanics problems involving inhomogeneously elastic solids split into three distinct layers

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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 2013年第Sep.期70卷 102-123页

作者： Chidlow, S. J. Teodorescu, M. Oxford Brookes Univ Dept Mech Engn & Math Sci Oxford OX33 1HX England Univ Calif Santa Cruz Baskin Sch Engn Santa Cruz CA 95064 USA

This paper investigates the frictionless two-dimensional contact problem of an inhomogeneously elastic material under a rigid punch. The inhomogeneous solid is deemed to comprise three distinct regions which represent a homogeneously elastic coating and substrate joined together by a functionally graded transition layer (interlayer) whose shear modulus depends exponentially on the vertical coordinate. We propose closed form solutions for the horizontal and vertical displacements of the solid which are analytic if the contact pressure is known exactly. These solutions are further used to derive a fast and efficient iterative algorithm from which the contact footprint resulting from the rigid stamp problem may be computed. A selection of numerical results are then presented using this method and it is found that our model compares well with those of other authors in the two particular limiting cases considered here. We then investigate the effects of material inhomogeneity and coating thickness on the cylindrical stamp problem and it is found that the maximum principal stress is highly dependent on the thickness and mechanical properties of the layer. In particular, it is found that the maximum principal stress that occurs in a material with a hard coating may be reduced by increasing the thickness of the transition layer whilst lower stresses are achieved in materials with soft coatings by decreasing interlayer thickness. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Contact mechanics Functionally graded materials Sub-surface stresses iterative algorithm

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Discrete-rate adaptive modulation with optimum switching thresholds for space-time coded multiple-input multiple-output system with imperfect channel state information

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IET COMMUNICATIONS 2013年第6期7卷 521-530页

作者： Yu, Xiangbin Tan, Wenting Leung, Shu-Hung Rui, Yun Yin, Xin Liu, Xiaoshuai Nanjing Univ Aeronaut & Astronaut Dept Elect Engn Nanjing Jiangsu Peoples R China City Univ Hong Kong Dept Elect Engn Hong Kong Hong Kong Peoples R China Chinese Acad Sci Shanghai Adv Res Inst Shanghai Peoples R China

The performance analysis of a space-time coded multiple-input multiple-output (MIMO) system with variable-rate adaptive modulation over flat Rayleigh fading channels for both perfect and imperfect channel state information (CSI) is presented. In this study, the optimum fading gain switching thresholds for attaining maximum spectrum efficiency (SE) subject to an average bit error rate (BER) constraint are derived. The existence and uniqueness of the Lagrange multiplier in the constrained SE optimisation is studied. It is shown that the Lagrange multiplier does exist and is unique for imperfect CSI. On the other hand, the Lagrange multiplier will be unique if the existence condition for MIMO under perfect CSI is satisfied. A practical iterative algorithm based on Newton's method for finding the Lagrange multiplier is proposed. By the switching thresholds, closed-form expressions of the SE and average BER are obtained. Simulation results for SE and BER are in good agreement with the theoretical analysis. The results show that the space-time block coded MIMO system using adaptive modulation (AM-STBC-MIMO) with average BER constraint provides SE better than AM-STBC-MIMO with fixed thresholds, and AM-STBC-MIMO using a BER upper bound, but it has performance degradation in SE for imperfect CSI.

关键词： adaptive modulation error statistics MIMO communication Newton method Rayleigh channels space-time codes discrete-rate adaptive modulation space-time coded multiple-input multiple-output system MIMO variable-rate adaptive modulation flat Rayleigh fading channels imperfect channel state information optimum fading gain switching spectrum efficiency bit error rate BER Lagrange multiplier iterative algorithm Newton's method CSI SE adaptive modulation error statistics MIMO communication Newton method Rayleigh channels space-time codes discrete-rate adaptive modulation space-time coded multiple-input multiple-output system MIMO variable-rate adaptive modulation flat Rayleigh fading channels imperfect channel state information optimum fading gain switching spectrum efficiency bit error rate BER Lagrange multiplier iterative algorithm Newton's method CSI SE

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On the Convergence of the Vector-Fitting algorithm

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 2013年第4期61卷 1435-1443页

作者： Lefteriu, Sanda Antoulas, Athanasios C. INRIA APICS Team F-06902 Sophia Antipolis France Rice Univ Elect & Comp Engn Dept Houston TX 77005 USA Jacobs Univ Bremen Sch Engn & Sci D-28759 Bremen Germany

Vector fitting (VF), first published by Gustavesen and Semlyen in 1999, is widely used for constructing rational models from measured or full-wave electromagnetic simulated frequency-domain responses (S-, Y-, or Z-parameters). As pointed out by Grivet-Talocia and Bandinu in 2006, to date there is no convergence analysis of the pole relocation iteration in VF. The goal of this paper is to elucidate this issue. It will be shown that the iteration seeks the roots of a set of coupled multivariate rational equations. For noise-free measurements, it is shown that there is no iteration involved, assuming that the number of starting poles is chosen greater or equal to the order of the underlying system. For noisy data, the VF iteration may not find any solution due to the fact that all stationary points of the fixed point iteration are repelling. Therefore, in case the iteration does not converge, we propose to incorporate the Newton step in the VF iteration, thus guaranteeing local convergence. Lastly, we provide a short review of variable projection as an alternative to VF.

关键词： Convergence analysis iterative algorithm Sanathanan-Koerner (SK) iteration Steiglitz-McBride (StMcB) method variable projection (VARPRO) algorithm vector fitting (VF)

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Sparse principal component analysis by choice of norm

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JOURNAL OF MULTIVARIATE ANALYSIS 2013年第1期114卷 127-160页

作者： Qi, Xin Luo, Ruiyan Zhao, Hongyu Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA Yale Univ Dept Epidemiol & Publ Hlth New Haven CT 06520 USA

Recent years have seen the developments of several methods for sparse principal component analysis due to its importance in the analysis of high dimensional data. Despite the demonstration of their usefulness in practical applications, they are limited in terms of lack of orthogonality in the loadings (coefficients) of different principal components, the existence of correlation in the principal components, the expensive computation needed, and the lack of theoretical results such as consistency in high-dimensional situations. In this paper, we propose a new sparse principal component analysis method by introducing a new norm to replace the usual norm in traditional eigenvalue problems, and propose an efficient iterative algorithm to solve the optimization problems. With this method, we can efficiently obtain uncorrelated principal components or orthogonal loadings, and achieve the goal of explaining a high percentage of variations with sparse linear combinations. Due to the strict convexity of the new norm, we can prove the convergence of the iterative method and provide the detailed characterization of the limits. We also prove that the obtained principal component is consistent for a single component model in high dimensional situations. As illustration, we apply this method to real gene expression data with competitive results. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Sparse principal component analysis High-dimensional data Uncorrelated or orthogonal principal components iterative algorithm Consistency in high dimension

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On hybrid split problem and its nonlinear algorithms

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FIXED POINT THEORY AND APPLICATIONS 2013年第1期2013卷 1-20页

作者： He, Zhenhua Du, Wei-Shih Honghe Univ Dept Math Yunnan 661100 Peoples R China Natl Kaohsiung Normal Univ Dept Math Kaohsiung 824 Taiwan

In this paper, we study a hybrid split problem (HSP for short) for equilibrium problems and fixed point problems of nonlinear operators. Some strong and weak convergence theorems are established. MSC: 47J25, 47H09, 65... 详细信息

关键词： fixed point problem equilibrium problem hybrid split problem iterative algorithm strong (weak) convergence theorem

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iterative methods for constrained convex minimization problem in Hilbert spaces

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FIXED POINT THEORY AND APPLICATIONS 2013年第1期2013卷 1-18页

作者： Tian, Ming Huang, Li-Hua Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

In this paper, based on Yamada's hybrid steepest descent method, a general iterative method is proposed for solving constrained convex minimization problem. It is proved that the sequences generated by proposed implicit and explicit schemes converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality.

关键词： iterative algorithm constrained convex minimization nonexpansive mapping fixed point variational inequality

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GNM ordered variational inequality system with ordered Lipschitz continuous mappings in an ordered Banach space

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2013年第1期2013卷 1-11页

作者： Li, Hong-Gang Qiu, Dong Jin, Maoming Chongqing Univ Posts & Telecommun Coll Math & Phys Inst Appl Math Chongqing 400065 Peoples R China Changjiang Normal Univ Inst Nonlinear Anal Res Chongqing 400803 Peoples R China

The main purpose of this paper is to introduce and study a new class of generalized nonlinear mixed ordered variational inequalities systems with ordered Lipschitz continuous mappings in ordered Banach spaces. Then, applying the matrix analysis and the vector-valued mapping fixed point analysis method, an existence theorem of solutions for this kind of the system is established. Furthermore, based on the existence theorem and the new ordered B-restricted-accretive mappings, a general algorithm for solving the systems is introduced and applied to the approximation solvability of the systems on hand. The obtained results seem to be general in nature.

关键词： general nonlinear mixed ordered variational inequality system ordered Lipschitz continuous mappings B-restricted-accretive mappings iterative algorithm convergence ordered Banach space

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