An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solutio...An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solution of a general tridiagonal system of equations with diagonal dominance. It is not only easy to implement, but also can directly carry out parallel computation. Convergence results are obtained by analysing the linear system. Numerical experiments show that the theory is accurate and the scheme is valid and reliable.展开更多
How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linea...How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).展开更多
In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order...In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.展开更多
Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differenti...Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.展开更多
The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed...The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed. Also the optimal parameter is presented. Numerical results show that the proper choice of the preconditioner can lead to effective by the preconditioned Gauss-Seidel type iterative methods for solving linear systems.展开更多
In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-m...In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.展开更多
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
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
Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterativ...Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.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
In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
Based on the nonlinear characiers of the discrete problems of some ellipticalvariational inequalities, this paper presents a numerical iterative method, the schemesof which are pithy and converge rapidly The new metho...Based on the nonlinear characiers of the discrete problems of some ellipticalvariational inequalities, this paper presents a numerical iterative method, the schemesof which are pithy and converge rapidly The new method possesses a high efficiency. insolving such applied engineering problems as obstacle problems and .free boundary.problems arising in fluid lubrications.展开更多
Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial ...Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.展开更多
In this work, we applied two electromagnetic models for the characterization of a planar structure including a flat, thick copper conductor. Indeed the first model is consisted by modeling two metal ribbons without bu...In this work, we applied two electromagnetic models for the characterization of a planar structure including a flat, thick copper conductor. Indeed the first model is consisted by modeling two metal ribbons without bulkiness, placed one above the other at a distance of h<sub>2</sub> equal to the thickness of the thick conductor. This approach has been implemented and tested by the iterative method. The results of simulations have been compared with those calculated by the Ansoft HFSS software, and they are in good concordance, validating the method of analysis used. The second model is based on the calculation of the effective permittivity of the medium containing the thick conductor. This medium consists of a metallic region of complex relative permittivity , the rest of this medium is filled with air e<sub>r</sub><sub>2</sub> = 1. The effective permittivity e<sub>eff</sub> calculated from these two relative permittivity e<sub>r</sub><sub>2</sub> and . Comparing the simulation results of this new formulation of the iterative method with those calculated by the software Ansoft HFSS shows that they are in good matching which validates the second model.展开更多
The skin effect is an electromagnetic phenomenon that makes the current flows only on the surface of the conductors at high frequency. This article is based on the phenomenon to model a structure made in coplanar tech...The skin effect is an electromagnetic phenomenon that makes the current flows only on the surface of the conductors at high frequency. This article is based on the phenomenon to model a structure made in coplanar technology. In reality, these types of structures integrated metal layers of different thickness of copper (9 μm, 18 μm, 35 μm, 70 μm). The neglect of this parameter introduces errors, sometimes significant, in the numerical calculations. This is why an iterative method (FWCIP) based on the wave concept was restated. Validation of results was carried out by comparison with those calculated by Ansoft HFSS software and Agilent ADS Technology. They show a good matching.展开更多
In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the appr...In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.展开更多
The mathematical modeling of solar cells is essential for any optimization operation of the efficiency or the diagnosis of photovoltaic generator. The photovoltaic module is generally represented by an equivalent circ...The mathematical modeling of solar cells is essential for any optimization operation of the efficiency or the diagnosis of photovoltaic generator. The photovoltaic module is generally represented by an equivalent circuit whose parameters are experimentally calculated by using the characteristic current-tension, I-V. The precise determination of these parameters stays a challenge for the researchers, making to a big difference in the models and the digital methods dedicated to their characterizations. In the present paper, We are interested to characterize the parameters of single diode and two diodes models, in order to plan the behavior of the photovoltaic generator under real functioning conditions. We developed an identification method of the parameters using Newton Raphson method by using the software Matlab/Simulink. This method is the faster technique which allows the identification of several parameters and can be used in real time applications. The results of the proposed method show an accordance with the experimental and simulated characteristics of photovoltaic generator.展开更多
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ...An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.展开更多
In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear ...In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.展开更多
Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods....Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.展开更多
文摘An Alternating Group Explicit (AGE) iterative method with intrinsic parallelism is constructed based on an implicit scheme for the Regularized Long-Wave (RLW) equation. The method can be used for the iteration solution of a general tridiagonal system of equations with diagonal dominance. It is not only easy to implement, but also can directly carry out parallel computation. Convergence results are obtained by analysing the linear system. Numerical experiments show that the theory is accurate and the scheme is valid and reliable.
基金support provided by the Ministry of Science and Technology,Taiwan,ROC under Contract No.MOST 110-2221-E-019-044.
文摘How to accelerate the convergence speed and avoid computing the inversion of a Jacobian matrix is important in the solution of nonlinear algebraic equations(NAEs).This paper develops an approach with a splitting-linearizing technique based on the nonlinear term to reduce the effect of the nonlinear terms.We decompose the nonlinear terms in the NAEs through a splitting parameter and then linearize the NAEs around the values at the previous step to a linear system.Through the maximal orthogonal projection concept,to minimize a merit function within a selected interval of splitting parameters,the optimal parameters can be quickly determined.In each step,a linear system is solved by the Gaussian elimination method,and the whole iteration procedure is convergent very fast.Several numerical tests show the high performance of the optimal split-linearization iterative method(OSLIM).
文摘In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.
文摘Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.
基金Project supported by MOE's 2004 New Century Excellent Talent Program (NCET)the Applied Basic Research Foundations of Sichuan Province (No.05JY029-068-2)
文摘The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, is presented. Convergence of the preconditioned method applied to Z-matrices is discussed. Also the optimal parameter is presented. Numerical results show that the proper choice of the preconditioner can lead to effective by the preconditioned Gauss-Seidel type iterative methods for solving linear systems.
文摘In this paper, the asynchronous versions of classical iterative methods for solving linear systems of equations are considered. Sufficient conditions for convergence of asynchronous relaxed processes are given for H-matrix by which nor only the requirements of [3] on coefficient matrix are lowered, but also a larger region of convergence than that in [3] is obtained.
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].
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 National Natural Science Foundation of China(61272300)
文摘Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.
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.
文摘In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
文摘Based on the nonlinear characiers of the discrete problems of some ellipticalvariational inequalities, this paper presents a numerical iterative method, the schemesof which are pithy and converge rapidly The new method possesses a high efficiency. insolving such applied engineering problems as obstacle problems and .free boundary.problems arising in fluid lubrications.
基金the NSF of China Grants 91937301 and 41675060,the National Key Scientific and Technological Infrastructure Project"EarthLab",and the ONR Grants N000141712375 and N000142012449 to the University of Oklahoma(OU)The numerical experiments were performed at the OU supercomputer SchoonerCIMMS by NOAA/Office of Oceanic and Atmospheric Research under NOAA-OU Cooperative Agreement#NA110AR4320072,U.S.Department of Commerce.
文摘Two types of existing iterative methods for solving the nonlinear balance equation(NBE)are revisited.In the first type,the NBE is rearranged into a linearized equation for a presumably small correction to the initial guess or the subsequent updated solution.In the second type,the NBE is rearranged into a quadratic form of the absolute vorticity with the positive root of this quadratic form used in the form of a Poisson equation to solve NBE iteratively.The two methods are rederived by expanding the solution asymptotically upon a small Rossby number,and a criterion for optimally truncating the asymptotic expansion is proposed to obtain the super-asymptotic approximation of the solution.For each rederived method,two iterative procedures are designed using the integral-form Poisson solver versus the over-relaxation scheme to solve the boundary value problem in each iteration.Upon testing with analytically formulated wavering jet flows on the synoptic,sub-synoptic and meso-αscales,the iterative procedure designed for the first method with the Poisson solver,named M1a,is found to be the most accurate and efficient.For the synoptic wavering jet flow in which the NBE is entirely elliptic,M1a is extremely accurate.For the sub-synoptic wavering jet flow in which the NBE is mostly elliptic,M1a is sufficiently accurate.For the meso-αwavering jet flow in which the NBE is partially hyperbolic so its boundary value problem becomes seriously ill-posed,M1a can effectively reduce the solution error for the cyclonically curved part of the wavering jet flow,but not for the anti-cyclonically curved part.
文摘In this work, we applied two electromagnetic models for the characterization of a planar structure including a flat, thick copper conductor. Indeed the first model is consisted by modeling two metal ribbons without bulkiness, placed one above the other at a distance of h<sub>2</sub> equal to the thickness of the thick conductor. This approach has been implemented and tested by the iterative method. The results of simulations have been compared with those calculated by the Ansoft HFSS software, and they are in good concordance, validating the method of analysis used. The second model is based on the calculation of the effective permittivity of the medium containing the thick conductor. This medium consists of a metallic region of complex relative permittivity , the rest of this medium is filled with air e<sub>r</sub><sub>2</sub> = 1. The effective permittivity e<sub>eff</sub> calculated from these two relative permittivity e<sub>r</sub><sub>2</sub> and . Comparing the simulation results of this new formulation of the iterative method with those calculated by the software Ansoft HFSS shows that they are in good matching which validates the second model.
文摘The skin effect is an electromagnetic phenomenon that makes the current flows only on the surface of the conductors at high frequency. This article is based on the phenomenon to model a structure made in coplanar technology. In reality, these types of structures integrated metal layers of different thickness of copper (9 μm, 18 μm, 35 μm, 70 μm). The neglect of this parameter introduces errors, sometimes significant, in the numerical calculations. This is why an iterative method (FWCIP) based on the wave concept was restated. Validation of results was carried out by comparison with those calculated by Ansoft HFSS software and Agilent ADS Technology. They show a good matching.
文摘In this note we at first briefly review iterative methods for effectively approaching a root of an unknown multiplicity. We describe a first order, then a second order estimate for the multiplicity index m of the approached root. Next we present a second order, two-step method for iteratively nearing a root of an unknown multiplicity. Subsequently, we introduce a novel chord, or a two- step method, not requiring beforehand knowledge of the multiplicity index m of the sought root, nor requiring higher order derivatives of the equilibrium function, which is quadratically convergent for any , and then reverts to superlinear.
文摘The mathematical modeling of solar cells is essential for any optimization operation of the efficiency or the diagnosis of photovoltaic generator. The photovoltaic module is generally represented by an equivalent circuit whose parameters are experimentally calculated by using the characteristic current-tension, I-V. The precise determination of these parameters stays a challenge for the researchers, making to a big difference in the models and the digital methods dedicated to their characterizations. In the present paper, We are interested to characterize the parameters of single diode and two diodes models, in order to plan the behavior of the photovoltaic generator under real functioning conditions. We developed an identification method of the parameters using Newton Raphson method by using the software Matlab/Simulink. This method is the faster technique which allows the identification of several parameters and can be used in real time applications. The results of the proposed method show an accordance with the experimental and simulated characteristics of photovoltaic generator.
文摘An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
基金supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)the Shanghai Leading Academic Discipline Project (No. J50101)
文摘In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.
基金Project supported by the Natural Science Foundation of Liaoning Province of China (No.20022021)
文摘Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method (GAOR) is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.