The sensitivity of phase-shifting interferometers (PSIs) to vibration impairs their application in unsteady environment. iterative algorithms were developed to desensitise the effect of vibration on PSIs, but their de...
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The sensitivity of phase-shifting interferometers (PSIs) to vibration impairs their application in unsteady environment. iterative algorithms were developed to desensitise the effect of vibration on PSIs, but their desensitising capability is restricted by the estimated initial value. In this paper, a spatial carrier-assisted method is proposed, in which a wavefront phase retrieved from an additional spatial-carrier interferogram is used as the initial value. Because of the benefits of spatial carrier, vibration immunity and sign determination, iteration could converge to accurate value even when interferometers are under severe vibration. To reduce the possibility of transverse movement of the measured surface, subsampling strategy is further proposed to decrease the required tilt angle, with the additional benefit of decreasing the calculation time of iteration. Computer simulations and experiments are performed to verify the effectiveness of the proposed method. Results indicate that the vibration desensitising capability of an iterative algorithm is significantly enhanced by the proposed method. The proposed method improves the vibration desensitising capability with low cost and is thus highly compatible. (C) 2017 Elsevier Ltd. All rights reserved.
Classical Fourier-Bessel methodology fails when used to reconstruct helical structures with severe Bessel overlap on the layer lines. In the reconstruction of a peculiar type of double-layered helical tube of GDP-tubu...
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Classical Fourier-Bessel methodology fails when used to reconstruct helical structures with severe Bessel overlap on the layer lines. In the reconstruction of a peculiar type of double-layered helical tube of GDP-tubulin, we face the problem of Bessel overlap on all the layer lines due to the superposition of the Fourier components from the inner and outer layers of the tube. In order to decompose the Fourier terms of the inner and outer layers more than one image of the tubes must be combined and the orientations of their inner and outer layer helices must be determined. While there is no direct analytical method to determine these orientational parameters, we have devised all iterative Fourier-Bessel algorithm to calculate the correct orientations and thus allow us to obtain a reconstruction from multiple images of the double-layered tubes. The algorithm successfully works for the reconstruction of computer-modeled double-layered helical tubes as well as with real images obtained by cryo-electron microscopy. The algorithm has also been applied with very satisfactory results to the reconstruction of 13-protofilament microtubules, which is another helical structure that suffer Bessel overlap, suggesting its generality. (C) 2004 Elsevier Inc. All rights reserved.
In this paper, we extend the auxiliary variational inequality technique due to Ding and Yao [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Comp...
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In this paper, we extend the auxiliary variational inequality technique due to Ding and Yao [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Comput. Math. Appl. 49 (2005) 857-869] to develop iterative algorithms for finding the approximate solutions of a mixed quasi-variational-like inclusion problem (in short, MQVLIP) in the setting of Banach spaces. We first establish a result on the existence of a solution of the equilibrium problem by virtue of the Fan-KKM lemma. Then by using this result and a result by Ding and Tan [X.P. Ding, K.K. Tan, A minimax inequality with applications to existence of equilibrium point and fixed point theorems, Colloq. Math. 63 (2) (1992) 233-247], we derive the existence of a unique solution of MQVLIP and the existence of approximate solutions generated by the proposed algorithms. Moreover, we also provide the new criteria for convergence of approximate solutions to the exact solution of MQVLIP. (C) 2008 Elsevier Ltd. All rights reserved.
A matrix P is an element of R-nxn is called a generalized reflection matrix if P-T = P and P-2 = I. An n x n matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix...
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A matrix P is an element of R-nxn is called a generalized reflection matrix if P-T = P and P-2 = I. An n x n matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP. (A = -PAP). In this paper, three iterative algorithms are proposed for solving the linear matrix equation A(1)X(1)B(1) + A(2)X(2)B(2) = C over reflexive (anti-reflexive) matrices X-1 and X-2. When this matrix equation is consistent over reflexive (anti-reflexive) matrices, for any reflexive (anti-reflexive) initial iterative matrices, the reflexive (anti-reflexive) solutions can be obtained within finite iterative steps in the absence of roundoff errors. By the proposed iterative algorithms, the least Frobenius norm reflexive (anti-reflexive) solutions can be derived when spacial initial reflexive (anti-reflexive) matrices are chosen. Furthermore, we also obtain the optimal approximation reflexive (anti-reflexive) solutions to the given reflexive ( anti-reflexive) matrices in the solution set of the matrix equation. Finally, some numerical examples are presented to support the theoretical results of this paper. (C) 2009 Elsevier Ltd. All rights reserved.
作者：
Chagra, WassilaUniv Tunis El Manar
Lab Analyse Conception & Commande Syst Inst Preparatoire Etud Ingn El Manar LR11ES20Ecole Natl Ingn Tunis BP 37 Tunis 1002 Tunisia
The purpose of this paper is to achieve an exhaustive and generalized method for the accurate calculation of the linear system settling time. Thus, the classical settling time expressions for the second-order linear s...
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The purpose of this paper is to achieve an exhaustive and generalized method for the accurate calculation of the linear system settling time. Thus, the classical settling time expressions for the second-order linear systems are reviewed. Then, new expressions are proposed and developed for the step response of the second-order and for higher-order under-damped and over-damped linear systems. The proposed expressions are different from all the existing ones, and they are more accurate. In addition, iterative algorithms that can be easily implemented are proposed in order to achieve accurate calculation of the settling time. The accuracy of the new expressions and the proposed iterative algorithms are illustrated by several numerical simulation examples.
Interference alignment(IA)with symbol extensions in the quasi-static flat-fading K-user multipleinput multiple-output(MIMO)interference channel(IC)is considered in this *** general,long symbol extensions are required ...
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Interference alignment(IA)with symbol extensions in the quasi-static flat-fading K-user multipleinput multiple-output(MIMO)interference channel(IC)is considered in this *** general,long symbol extensions are required to achieve the optimal fractional degrees of freedom(DOF).However,long symbol extensions over orthogonal dimensions produce structured(diagonal or block diagonal)channel matrices from transmitters to *** of existing approaches are limited in cases where the channels have some special structures,because they align the interference without preserving the dimensionality of the desired signal *** overcome this common drawback of most existing IA algorithms,two novel iterative algorithms for IA with symbol extensions are *** first algorithm designs transceivers for IA based on the mean square error(MSE)criterion which minimizes the total MSE of the system while preserving the dimensionality of the desired *** novel IA algorithm is a constrained optimization problem which can be solved by Lagrangian *** convergence is proven as *** the reciprocity of alignment,the second algorithm is proposed based on the maximization of the multidimensional case of the generalized Rayleigh *** maximizes each receiver’s signal to interference plus noise ratio(SINR)while preserving the dimensionality of the desired *** simulation results,we show the superiority of the proposed algorithms in terms of four aspects,i.e.,average sum rate,the fraction of the interfering signal power in the desired signal subspace,bit error rate(BER)and the relative power of the weakest desired data stream.
In this paper we propose some iterative algorithms for the obstacle problems discretized by the finite difference method. We rewrite the obstacle problem to an equivalent complementarity problem. We use the regulariza...
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In this paper we propose some iterative algorithms for the obstacle problems discretized by the finite difference method. We rewrite the obstacle problem to an equivalent complementarity problem. We use the regularization trick to non-smooth absolute function. Then we apply the Newton's method to obtain an iterative algorithm. Some other two algorithms based on this algorithm are derived. Numerical experiments show the effective of the algorithm.
In this paper, we give the notion of P-eta-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous eta-subdifferentiable...
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In this paper, we give the notion of P-eta-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous eta-subdifferentiable proper functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a class of generalized set-valued variational-like inclusions in Banach space and show its equivalence with a class of implicit Wiener-Hopf equations using the concept of P-eta-proximal mapping. Using this equivalence, we propose a new class of iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solution of generalized set-valued variational-like inclusions and discuss the convergence criteria and the stability of the iterative algorithm. (c) 2004 Elsevier Inc. All rights reserved.
In this paper, we propose a new iterative algorithm and analyze it in detail inasmuch as convergence, stability, and data dependency for the class of almost contraction mappings. We also consider another iterative alg...
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In this paper, we propose a new iterative algorithm and analyze it in detail inasmuch as convergence, stability, and data dependency for the class of almost contraction mappings. We also consider another iterative algorithm called F* iterative algorithm proposed by Ali et al. (Comp. Appl. Math. 39, 267 (2020)) and derive some new algorithms from this with the aim of giving an affirmative answer to an open question raised by the same authors. Our results considerably improve the corresponding results in Ali et al. (Comp. Appl. Math. 39, 267 (2020)). We submit some non-trivial numerical examples to illustrate the robustness, feasibility, and effectiveness of our findings.
Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. Based on Paige's algorithms LSQR and residual-reducing version of LSQR proposed in Paige and...
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Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. Based on Paige's algorithms LSQR and residual-reducing version of LSQR proposed in Paige and Saunders [LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Softw. 8(1) (1982), pp. 4371], we provide two matrix iterative algorithms for finding solution with the least norm to the QLS problem by making use of structure of real representation matrices. Numerical experiments are presented to illustrate the efficiency of our algorithms.
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