In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of th...In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].展开更多
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is...In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.展开更多
An AOR(Accelerated Over-Relaxation)iterative method is suggested by introducing one more parameter than SOR(Successive Over-Relaxation)method for solving coupled Lyapunov matrix equations(CLMEs)that come from continuo...An AOR(Accelerated Over-Relaxation)iterative method is suggested by introducing one more parameter than SOR(Successive Over-Relaxation)method for solving coupled Lyapunov matrix equations(CLMEs)that come from continuous-time Markovian jump linear systems.The proposed algorithm improves the convergence rate,which can be seen from the given illustrative examples.The comprehensive theoretical analysis of convergence and optimal parameter needs further investigation.展开更多
Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at...Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at the base stations. However, the excessively high computational complexity of the signal detection in massive MIMO systems imposes a significant challenge for practical hardware implementations. In this paper, we propose a novel minimum mean square error(MMSE) signal detection using the accelerated overrelaxation(AOR) iterative method without complicated matrix inversion, which is capable of reducing the overall complexity of the classical MMSE algorithm by an order of magnitude. Simulation results show that the proposed AOR-based method can approach the conventional MMSE signal detection with significant complexity reduction.展开更多
This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods...This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.展开更多
Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced...Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.展开更多
Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often on...Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often only knowspartial independent rows of the least-squares system. To solve the least-squares all the measurements must be gathered at a centralized location and then perform the computa-tion. Such data collection and computation are inefficient because of bandwidth and time constraints and sometimes areinfeasible because of data privacy concerns. Iterative methods are natural candidates for solving the aforementionedproblem and there are many studies regarding this. However,most of the proposed solutions are related to centralized/parallel computations while only a few have the potential to beapplied in distributed networks. Thus distributed computations are strongly preferred or demanded in many of the realworld applications, e.g. smart-grid, target tracking, etc. Thispaper surveys the representative iterative methods for distributed least-squares in networks.展开更多
In the procedure of neutron fluence measurement in the whole energy range (10-4 eV^18 MeV), in the irra- diation chamber of a UZrH reactor, the neutron energy spectra are unfolded using the method of minimizing direct...In the procedure of neutron fluence measurement in the whole energy range (10-4 eV^18 MeV), in the irra- diation chamber of a UZrH reactor, the neutron energy spectra are unfolded using the method of minimizing directed divergence and SAND-II, which are used broadly at home and abroad. These methods belong to the iterative methods. In this article, the procedure of the spectra unfolding using the two methods is described in detail. The neutron spec- trum distribution unfolded by the two methods agree well with each other. In the end, the major differences of the two iterative methods are compared with each other, and the main factors affecting the accuracy of the spectra unfolding with the iterative method are discussed.展开更多
The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method conv...The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method converges, and the preconditioned method is invalid when the classical iterative method does not converge. The results in corresponding references are improved and perfected.展开更多
A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode...A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.展开更多
An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface. The multiple interaction of the scattering field is ch...An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface. The multiple interaction of the scattering field is characterized with the corrected electromagnetic currents of the wind-driven sea surface. The actual surface currents are approximated with the iterative solution of the corrected currents. A newly developed sea spectrum, Elfouhaily spectrum, is utilized to build the sea surface model. The shadowing correction is improved by the Dept-Buffer algorithm. The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.展开更多
The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenv...The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.展开更多
A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the sol...A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.展开更多
This paper givers an estimated formula of convergence rate for parallel multisplitting iterative method.Using the formula,we can simplify and unify the proof of convergence of PMI_method.
The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also app...The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.展开更多
This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification o...This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.展开更多
This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation＇s solution are obtained succe...This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation＇s solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.展开更多
The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models...The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.展开更多
To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to a...To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.展开更多
基金the Thailand Research Fund for financial support under Grant BRG5280016
文摘In this article, we introduce a new viscosity iterative method for two nonexpansive mappings in Hilbert spaces. We also prove, without commutativity assumption, that the iterates converge to a common fixed point of the mappings which solves some variational inequality. The results presented extend the corresponding results of Shimizu and Takahashi IT. Shimizu, W. Takahashi, Strong convergence to common fixed point of families of nonexpansive mappings, J. Math. Anal. Appl. 211 （1997）, 71-83], and Yao and Chen [Y. Yao, R. Chert, Convergence to common fixed points of average mappings without commutativity assumption in Hilbert spaces, Nonlinear Analysis 67（2007）, 1758-1763].
文摘In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.
基金Supported by Key Scientific Research Project of Colleges and Universities in Henan Province of China(Grant No.20B110012)。
文摘An AOR(Accelerated Over-Relaxation)iterative method is suggested by introducing one more parameter than SOR(Successive Over-Relaxation)method for solving coupled Lyapunov matrix equations(CLMEs)that come from continuous-time Markovian jump linear systems.The proposed algorithm improves the convergence rate,which can be seen from the given illustrative examples.The comprehensive theoretical analysis of convergence and optimal parameter needs further investigation.
基金supported by the key project of the National Natural Science Foundation of China (No. 61431001)Huawei Innovation Research Program, the 5G research program of China Mobile Research Institute (Grant No. [2015] 0615)+2 种基金the open research fund of National Mobile Communications Research Laboratory Southeast University (No.2017D02)Key Laboratory of Cognitive Radio and Information Processing, Ministry of Education (Guilin University of Electronic Technology)the Foundation of Beijing Engineering and Technology Center for Convergence Networks and Ubiquitous Services, and Keysight
文摘Massive multiple-input multiple-output(MIMO) system is capable of substantially improving the spectral efficiency as well as the capacity of wireless networks relying on equipping a large number of antenna elements at the base stations. However, the excessively high computational complexity of the signal detection in massive MIMO systems imposes a significant challenge for practical hardware implementations. In this paper, we propose a novel minimum mean square error(MMSE) signal detection using the accelerated overrelaxation(AOR) iterative method without complicated matrix inversion, which is capable of reducing the overall complexity of the classical MMSE algorithm by an order of magnitude. Simulation results show that the proposed AOR-based method can approach the conventional MMSE signal detection with significant complexity reduction.
基金This work was supported by the National Natural Science Foundation of China
文摘This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.
基金supported by the Natural Science Foundation of China (Nos. 11971230, 12071215)the Fundamental Research Funds for the Central Universities(No. NS2018047)the 2019 Graduate Innovation Base(Laboratory)Open Fund of Jiangsu Province(No. Kfjj20190804)
文摘Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.
基金partially supported by US NSF under Grant No.NSF-CNS-1066391and No.NSF-CNS-0914371,NSF-CPS-1135814 and NSF-CDI-1125165
文摘Many science and engineering applications involve solvinga linear least-squares system formed from some field measurements. In the distributed cyber-physical systems(CPS),each sensor node used for measurement often only knowspartial independent rows of the least-squares system. To solve the least-squares all the measurements must be gathered at a centralized location and then perform the computa-tion. Such data collection and computation are inefficient because of bandwidth and time constraints and sometimes areinfeasible because of data privacy concerns. Iterative methods are natural candidates for solving the aforementionedproblem and there are many studies regarding this. However,most of the proposed solutions are related to centralized/parallel computations while only a few have the potential to beapplied in distributed networks. Thus distributed computations are strongly preferred or demanded in many of the realworld applications, e.g. smart-grid, target tracking, etc. Thispaper surveys the representative iterative methods for distributed least-squares in networks.
文摘In the procedure of neutron fluence measurement in the whole energy range (10-4 eV^18 MeV), in the irra- diation chamber of a UZrH reactor, the neutron energy spectra are unfolded using the method of minimizing directed divergence and SAND-II, which are used broadly at home and abroad. These methods belong to the iterative methods. In this article, the procedure of the spectra unfolding using the two methods is described in detail. The neutron spec- trum distribution unfolded by the two methods agree well with each other. In the end, the major differences of the two iterative methods are compared with each other, and the main factors affecting the accuracy of the spectra unfolding with the iterative method are discussed.
文摘The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method converges, and the preconditioned method is invalid when the classical iterative method does not converge. The results in corresponding references are improved and perfected.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90111011 and 10471039）, the National Key Basic Research Special Foundation of China （Grant Nos 2003CB415101-03 and 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （Grant No KZCX3-SW-221） and in part by E-Institutes of Shanghai Municipal Education Commission （Grant No N.E03004）.
文摘A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.
基金Project supported by the National Natural Science Foundation of China(Grant No.60871070)the National Pre-research Foundation and the Foundation of National Electromagnetic Scattering Laboratory,China
文摘An iterative method in the Kirchhoff approximation is proposed for high frequency multiple electromagnetic scattering from two-dimensional dielectric sea surface. The multiple interaction of the scattering field is characterized with the corrected electromagnetic currents of the wind-driven sea surface. The actual surface currents are approximated with the iterative solution of the corrected currents. A newly developed sea spectrum, Elfouhaily spectrum, is utilized to build the sea surface model. The shadowing correction is improved by the Dept-Buffer algorithm. The validity of the iterative Kirchhoff approximation is verified by the agreement of backscattering coefficients with the measured data.
文摘The relativistic Duffin-Kemmer-Petiau equation in the presence of Hulthen potential in （1 ＋2） dimensions for spin-one particles is studied. Hence, the asymptotic iteration method is used for obtaining energy eigenvalues and eigenfunctions.
文摘A new iterating method based on homotopy function is developed in this paper. All solutions can be found easily without the need of choosing proper initial values. Compared to the homotopy continuation method, the solution process of the present method is simplified, and the computation efficiency as well as the reliability for obtaining all solutions is also improved. By application of the method to the mechanisms problems, the results are satisfactory.
文摘This paper givers an estimated formula of convergence rate for parallel multisplitting iterative method.Using the formula,we can simplify and unify the proof of convergence of PMI_method.
文摘The asymptotic iteration method （AIM） is used to obtain the quasi-exact solutions of the Schr6dinger equation with a deformed well potential. For arbitrary potential parameters, a numerical aspect of AIM is also applied to obtain highly accurate energy eigenvalues. Additionally, the perturbation expansion, based on the AIM approach, is utilized to obtain simple analytic expressions for the energy eigenvalues.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10771019 and 10826107)
文摘This paper applies the variational iteration method to obtain approximate analytic solutions of compressible Euler equations in gas dynamics. This method is based on the use of Lagrange multiplier for identification of optimal values of parameters in a functional. Using this method, a rapid convergent sequence is produced which converges to the exact solutions of the problem. Numerical results and comparison with other two numerical solutions verify that this method is very convenient and efficient.
基金supported by the National Natural Science Foundation of China (Grant Nos.41105063 and 61070041)
文摘This paper studies a delayed air-sea coupled oscillator describing the physical mechanism of El Nino Southern Oscillation. The approximate expansions of the delayed differential equation＇s solution are obtained successfully by the modified variational iteration method. The numerical results illustrate the effectiveness and correctness of the method by comparing with the exact solution of the reduced model.
基金Project supported by the Key Program of the National Natural Science Foundation of China （Grant No. 51134018）.
文摘The variational iteration method is successfully extended to the case of solving fractional differential equations, and the Lagrange multiplier of the method is identified in a more accurate way. Some diffusion models with fractional derivatives are investigated analytically, and the results show the efficiency of the new Lagrange multiplier for fractional differential equations of arbitrary order.
基金The National Natural Science Founda-tion of China ( No.70471039)the National Social Science Foundation of China (No.07BJY038)the Program for New Century Excellent Talents in University (No.NCET-04-0886)
文摘To solve vehicle routing problem with different fleets, two methodologies are developed. The first methodology adopts twophase strategy. In the first phase, the improved savings method is used to assign customers to appropriate vehicles. In the second phase, the iterated dynasearch algorithm is adopted to route each selected vehicle with the assigned customers. The iterated dynasearch algorithm combines dynasearch algorithm with iterated local search algorithm based on random kicks. The second methodplogy adopts the idea of cyclic transfer which is performed by using dynamic programming algorithm, and the iterated dynasearch algorithm is also embedded in it. The test results show that both methodologies generate better solutions than the traditional method, and the second methodology is superior to the first one.
