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Variational Bayesian-Based iterative algorithm for ARX Models with Random Missing Outputs

CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2018年第4期37卷 1594-1608页

作者： Chen, Jing Liu, Yanjun Jiangnan Univ Sch Sci Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China

In this paper, a variational Bayesian (VB)-based iterative algorithm for ARX models with random missing outputs is proposed. The distributions of missing outputs can be estimated in the VB-E step, and the distributions of unknown parameters can be estimated in the VB-M step by the estimated missing outputs and the available outputs. Compared with the expectation-maximization-based iterative algorithm, this algorithm computes the latent variable and the parameter distributions at each iteration. Therefore, it is more accurate. The simulation results demonstrate the advantages of the proposed algorithm.

关键词： Parameter estimation Missing outputs Variational Bayesian approach ARX model iterative algorithm

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Convergence and stability of an iterative algorithm for a system of generalized implicit variational-like inclusions in Banach spaces

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APPLIED MATHEMATICS AND COMPUTATION 2012年第18期218卷 9208-9219页

作者： Kazmi, K. R. Ahmad, Naeem Shahzad, Mohammad Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India Aligarh Muslim Univ Dept Appl Math Aligarh 202002 Uttar Pradesh India

In this paper, we give the notion of M-eta-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space, which is an extension of proximal mappings studied in [X. P. Ding, F. Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369-383;K. R. Kazmi, M. I. Bhat, Convergence and stability of iterative algorithms of generalized set-valued variational-like inclusions in Banach spaces, Appl. Math. Comput. 113 (2005) 153-165;K. R. Kazmi, M. I. Bhat, N. Ahmad, An iterative algorithm based on M-proximal mappings for a system of generalized implicit variational inclusions in Banach spaces, J. Comput. Appl. Math. 233 (2009) 361-371]. We prove its existence and Lipschitz continuity in reflexive Banach space. Further, we consider a system of generalized implicit variational-like inclusions in Banach spaces and show its equivalence with a system of implicit equations using the concept of M-eta-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational-like inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational-like inclusions and discuss the convergence and stability analysis of the iterative algorithm in the setting of uniformly smooth Banach spaces. (C) 2012 Elsevier Inc. All rights reserved.

关键词： System of generalized implicit variational-like inclusions M-eta-proximal mapping System of implicit equations iterative algorithm Convergence and stability analysis

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Strong convergence of an iterative algorithm for variational inequalities in Banach spaces

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MATHEMATICAL AND COMPUTER MODELLING 2011年第1-2期54卷 325-329页

作者： Yao, Yonghong Maruster, Stefan Tianjin Polytech Univ Dept Math Tianjin 300160 Peoples R China W Univ Timisoara Timisoara Romania

In this paper, we construct a new simple algorithm for solving some variational inequality in Banach spaces. Furthermore, we prove that the proposed algorithm has strong convergence. (C) 2011 Elsevier Ltd. All rights ... 详细信息

关键词： iterative algorithm Variational inequality Strong convergence Banach spaces

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An iterative algorithm for approximating convex minimization problem

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期188卷 648-656页

作者： Yao, Yonghong Liou, Yeong-Cheng Yao, Jen-Chih Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan Cheng Shiu Univ Dept Informat Management Kaohsiung 833 Taiwan Tianjin Polytech Univ Dept Math Tianjin 300160 Peoples R China

We suggest and analyze an iterative algorithm without the assumption of any type of commutativity on an infinite family of nonexpansive mappings. We show that the proposed iterative algorithm converges to the unique minimizer of some quadratic function over the common fixed point sets of an infinite family of nonexoansive mappings. Our result extend and improve many results announced by many authors. (C) 2006 Elsevier Inc. All rights reserved.

关键词： nonexpansive mapping fixed point convex minimization problem iterative algorithm

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Linearization for Microwave Photonic OFDM Transmission Systems Using an iterative algorithm Based on FEC Mechanism

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2022年第15期40卷 5013-5020页

作者： Chen, Yu Chen, Yang East China Normal Univ Shanghai Key Lab Multidimens Informat Proc Shanghai 200241 Peoples R China East China Normal Univ Engn Ctr SHMEC Space Informat & GNSS Shanghai 200241 Peoples R China

A digital linearization algorithm is proposed to reduce the third-order intermodulation distortion (IMD3) for the microwave photonic (MWP) orthogonal frequency-division multiplexing (OFDM) transmission system with intensity modulation and direct detection. Forward error correction (FEC) is added to the OFDM signal to suppress the IMD3 in conjunction with an iterative operation. The distorted OFDM signal from the MWP system goes through iterative operations including fast Fourier transform, demodulation, error correction, signal reconstruction, and interference cancellation until the output converges. Compared with the non-iterative method and the iterative method without FEC mechanism, the proposed method has a significant advantage in linearizing signals with large nonlinearity and low signal-to-noise ratio. 200-Msym/s 64 quadrature-amplitude modulation (64-QAM) OFDM signals with a large peak-to-peak voltage of 650 mV are amplified by a power amplifier and then input to the MWP link and linearized by the FEC-based iterative method. The results show that the error vector magnitudes (EVMs) of the OFDM signals can be optimized from 13.1% to 2.9% and from 13.4% to 6.3% when the output E-b/N-0 from the MWP link is about 35 dB and 13.5 dB, respectively. Besides, a 3-GHz 64-QAM OFDM signal is successfully transmitted through a 25-km standard single-mode fiber with an EVM of 3.9% after linearization.

关键词： OFDM iterative methods Interference Forward error correction Optical distortion Signal to noise ratio Codes Digital signal processing forward error correction iterative algorithm linearization third-order intermodulation distortion

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Existence and iterative algorithm of solutions for a system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems in Banach spaces

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2010年第1-2期33卷 209-225页

作者： Wang, Zhong Bao Ding, Xie Ping Sichuan Univ Coll Math Chengdu 610064 Sichuan Peoples R China Sichuan Normal Univ Coll Math & Software Sci Chengdu 610066 Sichuan Peoples R China

In this paper, we introduce and study a new system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Firstly, we prove the existence and uniqueness of solutions of the auxiliary problems for the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems. Secondly, an iterative algorithm for solving the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems is constructed by using this existence and uniqueness result. Finally, we show the existence of solutions of the system of generalized set-valued strongly nonlinear mixed variational-like inequalities problems and discuss the convergence analysis of this algorithm. These results improve, unify and generalize many corresponding known results given in literatures.

关键词： System of generalized set-valued strongly nonlinear mixed variational-like inequalities problems Auxiliary principle iterative algorithm Reflexive Banach spaces

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A gradient based iterative algorithm for solving structural dynamics model updating problems

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MECCANICA 2013年第9期48卷 2245-2253页

作者： Yuan, Yongxin Liu, Hao Jiangsu Univ Sci & Technol Sch Math & Phys Zhenjiang 212003 Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 210016 Jiangsu Peoples R China

The procedure of updating an existing but inaccurate model is an essential step toward establishing an effective model. Updating damping and stiffness matrices simultaneously with measured modal data can be mathematically formulated as following two problems. Problem 1: Let M (a) aSR (nxn) be the analytical mass matrix, and I >=diag{lambda (1),aEuro broken vertical bar,lambda (p) }aC (pxp) , X=[x (1),aEuro broken vertical bar,x (p) ]aC (nxp) be the measured eigenvalue and eigenvector matrices, where rank(X)=p, p < n and both I > and X are closed under complex conjugation in the sense that , for j=1,aEuro broken vertical bar,l, and lambda (k) aR, x (k) aR (n) for k=2l+1,aEuro broken vertical bar,p. Find real-valued symmetric matrices D and K such that M (a) XI > (2)+DXI >+KX=0. Problem 2: Let D (a) ,K (a) aSR (nxn) be the analytical damping and stiffness matrices. Find such that , where S (E) is the solution set of Problem 1 and ayena <...ayen is the Frobenius norm. In this paper, a gradient based iterative (GI) algorithm is constructed to solve Problems 1 and 2. A sufficient condition for the convergence of the iterative method is derived and the range of the convergence factor is given to guarantee that the iterative solutions consistently converge to the unique minimum Frobenius norm symmetric solution of Problem 2 when a suitable initial symmetric matrix pair is chosen. The algorithm proposed requires less storage capacity than the existing numerical ones and is numerically reliable as only matrix manipulation is required. Two numerical examples show that the introduced iterative algorithm is quite efficient.

关键词： Model updating iterative algorithm Damped structural system Partially prescribed spectral data Optimal approximation

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An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2013年第2期54卷 399-416页

作者： Loris, Ignace Verhoeven, Caroline Univ Libre Bruxelles Brussels Belgium

We propose an iterative algorithm for the minimization of a a"" (1)-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in the penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.

关键词： Inverse problems Sparsity Convex optimization iterative algorithm Wavelets Magneto-encephalography

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A robust reputation iterative algorithm based on Z-statistics in a rating system with thorny objects

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2023年第6期74卷 1600-1612页

作者： Zhu, Huan Xiao, Yu Wang, Zhi-Gang Wu, Jun Beijing Normal Univ Int Acad Ctr Complex Syst Zhuhai 519087 Peoples R China Beijing Normal Univ Sch Syst Sci Beijing Peoples R China Natl Univ Def Technol Beijing Interdisciplinary Res Ctr Changsha Peoples R China

With the explosive growth of online alternative objects, the availability of a credible rating system could play a valuable role for users who are evaluating and/or choosing items. Due to the existence of spammers, many methods have been proposed that employ a reputation-based mechanism in the last few years. However, these methods only consider spammers' behaviours but neglect the effect of thorny objects, which are difficult to evaluate because of their intrinsic uncertainty and complexity with respect to the problem context, knowledge gaps, and various user criteria. To solve this problem, we propose a new reputation iterative algorithm based on Z-statistics (ZS), which eliminates the effect of thorny objects and strengthens the ability to deal with spammers. In this article, the proposed method makes effectiveness comparisons with other typical methods using a rating example and a simulated rating system, and presents additional effectiveness and complexity analyses of these results. Finally, the experimental results also demonstrate that the ZS algorithm outperforms other methods in simultaneously dealing with the effects of spammers and thorny objects.

关键词： Rating system iterative algorithm user reputation Z-statistics robustness

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A Low Complexity iterative algorithm for Joint Zero Diagonalization

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IEEE SIGNAL PROCESSING LETTERS 2012年第2期19卷 115-118页

作者： Zhang, Wei-Tao Lou, Shun-Tian Xidian Univ Sch Elect Engn Xian 710071 Peoples R China

In this letter, we introduce a fast and computationally efficient iterative algorithm for joint zero diagonalization of a set of complex-valued target matrices. The proposed algorithm is actually a low complexity version of FJZD algorithm, it has a computational complexity of O(KN2), where K and N and are the number and dimension of the target matrices respectively. Moreover, the proposed algorithm is superior to FJZD in terms of interference to signal ratio. Simulation results demonstrate the good performance of the proposed algorithm.

关键词： Complex value complexity iterative algorithm joint zero diagonalization

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