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Least Squares Approach to Joint Beam Design for Interference Alignment in Multiuser Multi-Input Multi-Output Interference Channels

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第9期58卷 4960-4966页

作者： Yu, Heejung Sung, Youngchul Korea Adv Inst Sci & Technol Dept Elect Engn Taejon 305701 South Korea

In this correspondence, the problem of interference alignment for K-user time-invariant multi-input multi-output interference channels is considered. The necessary and sufficient conditions for interference alignment are converted to a system of linear equations that have dummy variables. Based on this linear system, a new algorithm for beam design for interference alignment is proposed by minimizing the overall interference misalignment. The proposed algorithm consists of solving a least squares problem iteratively. The convergence of the proposed algorithm is established, and its complexity is analyzed. The performance of the proposed algorithm is also evaluated numerically. It is shown that the proposed algorithm has faster convergence and lower complexity than the previous method with a comparable sum rate performance in the most practical case of two receive antennas.

关键词： Interference alignment interference channels iterative algorithm least squares multi-user MIMO

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Least squares solution with the minimum-norm to general matrix equations via iteration

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APPLIED MATHEMATICS AND COMPUTATION 2010年第10期215卷 3547-3562页

作者： Li, Zhao-Yan Wang, Yong Zhou, Bin Duan, Guang-Ren Harbin Inst Technol Ctr Control Theory & Guidance Technol Harbin 150001 Peoples R China Harbin Inst Technol Dept Math Harbin 150001 Peoples R China

Two iterative algorithms are presented in this paper to solve the minimal norm least squares solution to a general linear matrix equations including the well-known Sylvester matrix equation and Lyapunov matrix equation as special cases. The first algorithm is based on the gradient based searching principle and the other one can be viewed as its dual form. Necessary and sufficient conditions for the step sizes in these two algorithms are proposed to guarantee the convergence of the algorithms for arbitrary initial conditions. Sufficient condition that is easy to compute is also given. Moreover, two methods are proposed to choose the optimal step sizes such that the convergence speeds of the algorithms are maximized. Between these two methods, the first one is to minimize the spectral radius of the iteration matrix and explicit expression for the optimal step size is obtained. The second method is to minimize the square sum of the F-norm of the error matrices produced by the algorithm and it is shown that the optimal step size exits uniquely and lies in an interval. Several numerical examples are given to illustrate the efficiency of the proposed approach. (C) 2009 Elsevier Inc. All rights reserved.

关键词： iterative algorithm Gradient General linear matrix equations Minimal norm least squares Optimal step size Convergence rate

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A new class of variational inclusions with B-monotone operators in Banach spaces

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第8期233卷 1888-1896页

作者： Luo, Xue-ping Huang, Nan-jing Sichuan Univ Dept Math Chengdu 610064 Sichuan Peoples R China

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. For solving such class of variational inclusions, we introduce a new notion of B-monotone operator and prove the Lipschitz continuity of the proximal mapping associated with the B-monotone operator. By using the proximal mapping, an iterative algorithm for solving such class of variational inclusions is constructed in Banach spaces. Under some suitable conditions, we prove the convergence of iterative sequence generated by the algorithm. (C) 2009 Elsevier B.V. All rights reserved.

关键词： B-monotone operator Proximal mapping iterative algorithm Variational inclusion Convergence

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Lifting construction based on Bernstein bases and application in image compression

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IET IMAGE PROCESSING 2010年第5期4卷 385-402页

作者： Yang, X. Zhu, Z. Guo, Y. Quan, Z. Beihang Univ Dept Math LMIB Minist Educ Beijing 100083 Peoples R China

A novel framework for the construction of biorthogonal wavelets based on Bernstein bases with an arbitrary order of vanishing moments using the lifting scheme is proposed. We explore the field of application of it in still image compression. The major contributions of this work can be summarised highlighting the following three aspects. First and foremost, we propose an algorithm that is used to increase the vanishing moments of wavelets from biorthogonal symmetrical wavelets based on Bernstein bases by the lifting scheme. An iterative algorithm for designing the lifting scheme is proposed, which is based on the relationship between the vanishing moments of the wavelet and multiples of zeros of z = 1. The authors provide formulas of the lifting scheme for the construction of wavelets with an arbitrary order of vanishing moments. In addition, the lifting scheme is the shortest among the lifting schemes with the same order of vanishing moments increasing and, more importantly, it is the only one possible. Second, to guarantee the symmetry of the lifting (dual lifting) biorthogonal filters, explicit formulas of the lifting scheme with an arbitrary order of vanishing moments are introduced, which simultaneously have the above two characteristics. With our method, a new family of the parameterisation with symmetry of filters and the related library of biorthogonal symmetric waveforms are presented. Finally, we present a new transform rule aiming at image compression and its corresponding algorithm. Applying the parameterisation of filters constructed in this paper, by adjusting their coefficients, we can realise the transform rule and obtain a new transform. We explore the possibility of applying the presented transforms in image compression at different compression rates, and the results of the experiments prove to be comparable with the CDF9/7 and several state-of-the-art wavelet transforms.

关键词： Computer vision and image processing techniques Bernstein bases Image and video coding biorthogonal filter image coding wavelet transforms lifting construction iterative methods Interpolation and function approximation (numerical analysis) image compression iterative algorithm Integral transforms data compression biorthogonal symmetrical wavelets

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An iterative algorithm to quantify factors influencing peptide fragmentation during tandem mass spectrometry

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Journal of bioinformatics and computational biology 2007年第2A期5卷 297-311页

作者： Chungong Yu Yu Lin Shiwei Sun Jinjin Cai Jingfen Zhang Dongbo Bu Zhuo Zhang Runsheng Chen Bioinformatics Lab Institute of Computing Technology Chinese Academy of Sciences Beijing 100080 China. yu_cg@***

In protein identification by tandem mass spectrometry, it is critical to accurately predict the theoretical spectrum for a peptide sequence. To date, the widely-used database searching methods adopted simple statistical models for predicting. For some peptide, these models usually yield a theoretical spectrum with a significant deviation from the experimental one. In this paper, in order to derive an improved predicting model, we utilized a non-linear programming model to quantify the factors impacting peptide fragmentation. Then, an iterative algorithm was proposed to solve this optimization problem. Upon a training set of 1803 spectra, the experimental result showed a good agreement with some known principles about peptide fragmentation, such as the tendency to cleave at the middle of peptide, and Pro's preference of the N-terminal cleavage. Moreover, upon a testing set of 941 spectra, comparison of the predicted spectra against the experimental ones showed that this method can generate reasonable predictions. The results in this paper can offer help to both database searching and de novo methods.

关键词： Mass spectrum mobile proton hypothesis linear programming iterative algorithm

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An iterative method for a system of generalized mixed quasi-variational inclusions with (A, η)-monotone mappings

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APPLIED MATHEMATICS AND COMPUTATION 2010年第12期215卷 4256-4262页

作者： He, Xiahui Zhou, Yunshan Hunan Univ Coll Mech & Vehicle Engn Changsha 410082 Hunan Peoples R China

In this paper, we introduce and consider a new system of generalized mixed quasi-variational inclusions with (A, eta)-monotone mappings. We prove the convergence of a new iterative algorithm for this system of generalized mixed quasi-variational inclusions. Our results can be viewed as a refinement and improvement of the previously known results in the literature. (C) 2009 Elsevier Inc. All rights reserved.

关键词： (A, eta)-monotone mapping System of generalized mixed quasi-variational inclusions Resolvent operator method iterative algorithm

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Strong convergence for a minimization problem on points of equilibrium and common fixed points of an infinite family of nonexpansive mappings

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第11期73卷 3513-3524页

作者： Colao, Vittorio Marino, Giuseppe Univ Calabria Dipartimento Matemat I-87036 Arcavacata Di Rende CS Italy

Let H be a Hilbert space. Consider on H a sequence of nonexpansive mappings {T(n)} with common fixed points, an equilibrium function G, a contraction f with coefficient 0< alpha < 1 and a strongly positive linear bounded operator A with coefficient (gamma) over bar 0. Let 0 < gamma < (gamma) over bar/alpha We define a suitable Mann type algorithm which strongly converges to the unique solution of the minimization problem(x is an element of C) 1/2 (Ax,x) - h (x), where h is a potential function for f and C is the intersection of the equilibrium points and the common fixed points of the sequence {T(n)}. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Equilibrium problem Fixed point Nonexpansive mapping Variational inequality iterative algorithm Minimization problem

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The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第11期233卷 2876-2883页

作者： Ding, Xie Ping Wang, Zhong Bao 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 mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature. (C) 2009 Elsevier B.V. All rights reserved.

关键词： System of generalized set-valued mixed variational-like inequality problems Auxiliary principle iterative algorithm Reflexive Banach space

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Two strong convergence theorems for Bregman strongly nonexpansive operators in reflexive Banach spaces

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第1期73卷 122-135页

作者： Reich, Simeon Sabach, Shoham Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel

We study the convergence of two iterative algorithms for finding common fixed points of finitely many Bregman strongly nonexpansive operators in reflexive Banach spaces. Both algorithms take into account possible computational errors. We establish two strong convergence theorems and then apply them to the solution of convex feasibility, variational inequality and equilibrium problems. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Banach space Bregman distance Bregman firmly nonexpansive operator Bregman inverse strongly monotone operator Bregman projection Bregman strongly nonexpansive operator Convex feasibility problem Equilibrium problem iterative algorithm Legendre function Monotone operator Totally convex function Variational inequality

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Viscous and inviscid regularizations in a class of evolutionary partial differential equations

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JOURNAL OF COMPUTATIONAL PHYSICS 2010年第19期229卷 6676-6687页

作者： Camassa, Roberto Chiu, Pao-Hsiung Lee, Long Sheu, Tony W. H. Univ Wyoming Dept Math Laramie WY 82071 USA Univ N Carolina Dept Math Chapel Hill NC USA Inst Nucl Energy Res Nucl Engn Div Taoyuan Cty Taiwan Natl Taiwan Univ Dept Engn Sci & Ocean Engn Taipei 10764 Taiwan Natl Taiwan Univ TIMS Taipei 10764 Taiwan

We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization. An equation in this class of PDEs can be written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. A recently developed two-step iterative method (P.H. Chiu, L. Lee, T.W.H. Sheu, A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation,). Comput. Phys. 228 (2009) 8034-8052) is employed to study this class of PDEs. The method is in principle superior for PDE's in this class as it preserves their physical dispersive features. In particular, we focus on a Leray-type regularization (H.S. Bhat, R.C. Fetecau, A Hamiltonian regularization of the Burgers equation, J. Nonlinear Sci. 16 (2006) 615-638) of the Hopf equation proposed in alternative to the classical Burgers viscous term. We show that the regularization effects induced by the alternative model can be vastly different from those induced by Burgers viscosity depending on the smoothness of initial data in the limit of zero regularization. We validate our numerical scheme by comparison with a particle method which admits closed form solutions. Further effects of the interplay between the dispersive terms comprising the Leray-regularization are illustrated by solutions of equations in this class resulting from regularized Burgers equation by selective elimination of dispersive terms. (C) 2010 Elsevier Inc. All rights reserved.

关键词： Helmholtz equation iterative algorithm Leray-type regularization Hopt equation Regularized Burgers equation

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