Aim To discuss the basic CORDIC algorithm that can be applied to digital signal processing and its applying condition called convergence range.Methods In addition to the original basic equation, another group iterativ...Aim To discuss the basic CORDIC algorithm that can be applied to digital signal processing and its applying condition called convergence range.Methods In addition to the original basic equation, another group iterative equation was used to evaluate the correspondent values of input data that did not lie within the convergence range. Results and Conclusion The improved CORDIC algorithm removes the limits of the range of convergence and can adapt itself to the variations of input values. The correctness of improved CORDIC algorithms has been proved by calculating examples.展开更多
In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at eac...In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.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.
Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal...In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.展开更多
Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iterat...Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.展开更多
To solve the wave functions and energies of the groundstate of H＋2 ion an iteration procedure for N- dimensional potentials is applied. The iterative solutions are convergent nicely, which are comparable to earlier r...To solve the wave functions and energies of the groundstate of H＋2 ion an iteration procedure for N- dimensional potentials is applied. The iterative solutions are convergent nicely, which are comparable to earlier results based on variational methods.展开更多
The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for t...The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.展开更多
The wave iterative method is a numerical method used in the electromagnetic modeling of high frequency electronic circuits. The object of the authors＇ study is to improve the convergence speed of this method by addin...The wave iterative method is a numerical method used in the electromagnetic modeling of high frequency electronic circuits. The object of the authors＇ study is to improve the convergence speed of this method by adding a new algorithm based on filtering techniques. This method requires a maximum number of iterations, noted Nmax, to achieve the convergence to the optimal value. This number wilt be reduced in order to reduce the computing time. The remaining iterations until Nmax will be calculated by the new algorithm which ensures a rapid convergence to the optimal result.展开更多
For the Hermitian inexact Rayleigh quotient iteration （RQI）, we consider the local convergence of the inexact RQI with the Lanczos method for the linear systems involved. Some attractive properties are derived for t...For the Hermitian inexact Rayleigh quotient iteration （RQI）, we consider the local convergence of the inexact RQI with the Lanczos method for the linear systems involved. Some attractive properties are derived for the residual, whose norm is ξk, of the linear system obtained by the Lanczos method at outer iteration k ＋ 1. Based on them, we make a refined analysis and establish new local convergence results. It is proved that （i） the inexact RQI with Lanezos converges quadratically provided that ξk ≤ξ with a constant ξ≥） 1 and （ii） the method converges linearly provided that ξk is bounded by some multiple of 1/‖τk‖ with ‖τk‖ the residual norm of the approximate eigenpair at outer iteration k. The results are fundamentally different from the existing ones that always require ξk 〈 1, and they have implications on effective implementations of the method. Based on the new theory, we can design practical criteria to control ξk to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory and demonstrate that the inexact RQI with Lanczos is competitive to the inexact RQI with MINRES.展开更多
Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Tw...Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.展开更多
By introducing a deadwzone scheme, a new neural network based adaptive iterative learning control （ILC） （NN-AILC） scheme is presented for nonlinear discrete-time systems, where the NN weights are time-varying. The...By introducing a deadwzone scheme, a new neural network based adaptive iterative learning control （ILC） （NN-AILC） scheme is presented for nonlinear discrete-time systems, where the NN weights are time-varying. The most distinct contribution of the proposed NN-AILC is the relaxation of the identical conditions of initial state and reference trajectory, which are common requirements in traditional ILC problems. Convergence analysis indicates that the tracking error converges to a bounded ball, whose size is determined by the dead-zone nonlinearity. Computer simulations verify the theoretical results.展开更多
文摘Aim To discuss the basic CORDIC algorithm that can be applied to digital signal processing and its applying condition called convergence range.Methods In addition to the original basic equation, another group iterative equation was used to evaluate the correspondent values of input data that did not lie within the convergence range. Results and Conclusion The improved CORDIC algorithm removes the limits of the range of convergence and can adapt itself to the variations of input values. The correctness of improved CORDIC algorithms has been proved by calculating examples.
文摘In this paper, a new trust region algorithm for unconstrained LC1 optimization problems is given. Compare with those existing trust regiion methods, this algorithm has a different feature: it obtains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound, but by solving a system of linear equations. Thus it reduces computational complexity and improves computation efficiency. It is proven that this algorithm is globally convergent and locally superlinear under some conditions.
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.
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
文摘In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.
基金Foundation item： Projects（60835005, 90820302） supported by the National Natural Science Foundation of China Project（2007CB311001） supported by the National Basic Research Program of China
文摘Globally exponential stability （which implies convergence and uniqueness） of their classical iterative algorithm is established using methods of heat equations and energy integral after embedding the discrete iteration into a continuous flow. The stability condition depends explicitly on smoothness of the image sequence, size of image domain, value of the regularization parameter, and finally discretization step. Specifically, as the discretization step approaches to zero, stability holds unconditionally. The analysis also clarifies relations among the iterative algorithm, the original variation formulation and the PDE system. The proper regularity of solution and natural images is briefly surveyed and discussed. Experimental results validate the theoretical claims both on convergence and exponential stability.
基金Supported by National Natural Science Foundation of China under Grant No.10847001the SRF for ROCS,SEM,and Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘To solve the wave functions and energies of the groundstate of H＋2 ion an iteration procedure for N- dimensional potentials is applied. The iterative solutions are convergent nicely, which are comparable to earlier results based on variational methods.
基金the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,Chinathe Dawn Program Foundationin Shanghai
文摘The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature.
文摘The wave iterative method is a numerical method used in the electromagnetic modeling of high frequency electronic circuits. The object of the authors＇ study is to improve the convergence speed of this method by adding a new algorithm based on filtering techniques. This method requires a maximum number of iterations, noted Nmax, to achieve the convergence to the optimal value. This number wilt be reduced in order to reduce the computing time. The remaining iterations until Nmax will be calculated by the new algorithm which ensures a rapid convergence to the optimal result.
基金supported by National Basic Research Program of China(Grant No.2011CB302400)National Natural Science Foundation of China(Grant No.11071140)
文摘For the Hermitian inexact Rayleigh quotient iteration （RQI）, we consider the local convergence of the inexact RQI with the Lanczos method for the linear systems involved. Some attractive properties are derived for the residual, whose norm is ξk, of the linear system obtained by the Lanczos method at outer iteration k ＋ 1. Based on them, we make a refined analysis and establish new local convergence results. It is proved that （i） the inexact RQI with Lanezos converges quadratically provided that ξk ≤ξ with a constant ξ≥） 1 and （ii） the method converges linearly provided that ξk is bounded by some multiple of 1/‖τk‖ with ‖τk‖ the residual norm of the approximate eigenpair at outer iteration k. The results are fundamentally different from the existing ones that always require ξk 〈 1, and they have implications on effective implementations of the method. Based on the new theory, we can design practical criteria to control ξk to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory and demonstrate that the inexact RQI with Lanczos is competitive to the inexact RQI with MINRES.
基金National Natural Science Foundation of China (Grant Nos. 11271298 and 11362021)
文摘Based on the finite element method(FEM), some iterative methods related to different Reynolds numbers are designed and analyzed for solving the 2D/3D stationary incompressible magnetohydrodynamics(MHD) numerically. Two-level finite element iterative methods, consisting of the classical m-iteration methods on a coarse grid and corrections on a fine grid, are designed to solve the system at low Reynolds numbers under the strong uniqueness condition. One-level Oseen-type iterative method is investigated on a fine mesh at high Reynolds numbers under the weak uniqueness condition. Furthermore, the uniform stability and convergence of these methods with respect to equation parameters R_e, R_m, S_c, mesh sizes h, H and iterative step m are provided. Finally, the efficiency of the proposed methods is confirmed by numerical investigations.
基金supported by General Program (60774022)State Key Program (60834001) of National Natural Science Foundation of ChinaDoctoral Foundation of Qingdao University of Science & Technology (0022324)
文摘By introducing a deadwzone scheme, a new neural network based adaptive iterative learning control （ILC） （NN-AILC） scheme is presented for nonlinear discrete-time systems, where the NN weights are time-varying. The most distinct contribution of the proposed NN-AILC is the relaxation of the identical conditions of initial state and reference trajectory, which are common requirements in traditional ILC problems. Convergence analysis indicates that the tracking error converges to a bounded ball, whose size is determined by the dead-zone nonlinearity. Computer simulations verify the theoretical results.
