In this paper, we discuss some iterated method for solving the saddle point problem. We propose some new schemes and prove its convergence. The method has weaker convergence condition than the classic Uzawa method. Th...
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In this paper, we discuss some iterated method for solving the saddle point problem. We propose some new schemes and prove its convergence. The method has weaker convergence condition than the classic Uzawa method. The analysis is supported by numerical experiments. (c) 2005 Elsevier Inc. All rights reserved.
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 distribution...
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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.
In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min parallel to((A1XB1)(A2XB2)) - ((C1)(C2))parallel to over bisymmetric matrices. By this algorithm, for any ...
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In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min parallel to((A1XB1)(A2XB2)) - ((C1)(C2))parallel to over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X-0, a solution X* can be obtained infinite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution (X) over cap to a given matrix (X) over bar in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation. (C) 2009 Elsevier Ltd. All rights reserved.
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. ...
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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.
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 ...
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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 reserved.
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 m...
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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.
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 int...
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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.
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...
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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.
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 mathematic...
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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.
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 multipli...
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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.
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