The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical h...The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.展开更多
Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are comp...Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.展开更多
In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the ...In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.展开更多
In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously pe...In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.展开更多
A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly ...A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.展开更多
An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors...An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.展开更多
The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumptio...The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved. Numerical experiments showed that the non-monotone line search was more effective.展开更多
We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on t...The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on the assumption that a well-defined physiological signal which also has a smooth form "hides" inside the noisy EEG signal, a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented. Firstly, the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM. Secondly, the preprocessed signals were classified by SVM method. The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.展开更多
Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improv...Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.展开更多
With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an effi...With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square (WLS) method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio (SNR) is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound (CRLB) accuracy for both near-field and far-field sources.展开更多
The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational in...The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.展开更多
Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presen...Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.展开更多
In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treat...In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.展开更多
A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this...A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals.展开更多
In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two...In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.展开更多
Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mine...Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system (BTS) of Thai- land with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.展开更多
文摘The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.
基金Supported by the National Natural Science Foundation of China(No.61574099)
文摘Quasi-Newton methods are the most widely used methods to find local maxima and minima of functions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithmetic cores, field programmable gate array(FPGA) has become an attractive alternative to the acceleration of scientific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton(DFP-QN) method by proposing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.
文摘In this paper, the non-quasi-Newton's family with inexact line search applied to unconstrained optimization problems is studied. A new update formula for non-quasi-Newton's family is proposed. It is proved that the constituted algorithm with either Wolfe-type or Armijotype line search converges globally and Q-superlinearly if the function to be minimized has Lipschitz continuous gradient.
基金supported by National Natural Science Foundation of China(Grant No.61761011)Natural Science Foundation of Guangxi(Grant No.2020GXNSFBA297078).
文摘In the graph signal processing(GSP)framework,distributed algorithms are highly desirable in processing signals defined on large-scale networks.However,in most existing distributed algorithms,all nodes homogeneously perform the local computation,which calls for heavy computational and communication costs.Moreover,in many real-world networks,such as those with straggling nodes,the homogeneous manner may result in serious delay or even failure.To this end,we propose active network decomposition algorithms to select non-straggling nodes(normal nodes)that perform the main computation and communication across the network.To accommodate the decomposition in different kinds of networks,two different approaches are developed,one is centralized decomposition that leverages the adjacency of the network and the other is distributed decomposition that employs the indicator message transmission between neighboring nodes,which constitutes the main contribution of this paper.By incorporating the active decomposition scheme,a distributed Newton method is employed to solve the least squares problem in GSP,where the Hessian inverse is approximately evaluated by patching a series of inverses of local Hessian matrices each of which is governed by one normal node.The proposed algorithm inherits the fast convergence of the second-order algorithms while maintains low computational and communication cost.Numerical examples demonstrate the effectiveness of the proposed algorithm.
文摘A balancing technique for casting or forging parts to be machined is presented in this paper.It allows an optimal part setup to make sure that no shortage of material(undercut)will occur during machining.Particularly in the heavy part in- dustry,where the resulting casting size and shape may deviate from expectations,the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined.The alignment is an iterative process involving nonlinear con- strained optimization,which forces data points to lie outside the nominal model under a specific order of priority.Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing.In this paper, Newton methods are applied to the balancing of blank part.The aforesaid algorithm is demonstrated in term of a marine propeller blade,and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.
基金Project supported by the National Natural Science Foundation of China (No. 10372014).
文摘An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.
基金Sponsored by Natural Science Foundation of Beijing Municipal Commission of Education(Grant No.KM200510028019).
文摘The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved. Numerical experiments showed that the non-monotone line search was more effective.
文摘We present an improved method. If we assume that the objective function is twice continuously differentiable and uniformly convex, we discuss global and superlinear convergence of the improved quasi-Newton method.
基金The paper was supported by Jiangsu Education Nature Foundation(06KJD310050,06KJB520022)
文摘The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI). Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI, based on the assumption that a well-defined physiological signal which also has a smooth form "hides" inside the noisy EEG signal, a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented. Firstly, the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM. Secondly, the preprocessed signals were classified by SVM method. The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.
文摘Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mmx750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 ram^380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear fimctions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel. It only takes 50% iterations compared to that of DA. The proposed method can serve a faster mold contour compensation method for sheet metal forming.
基金supported by the Major National Science&Technology Projects(2010ZX03006-002-04)the National Natural Science Foundation of China(61072070)+4 种基金the Doctorial Programs Foundation of the Ministry of Education(20110203110011)the"111 Project"(B08038)the Fundamental Research Funds of the Ministry of Education(72124338)the Key Programs for Natural Science Foundation of Shanxi Province(2012JZ8002)the Foundation of State Key Laboratory of Integrated Services Networks(ISN1101002)
文摘With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival (TDOAs) and gain ratios of arrival (GROAs), an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square (WLS) method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio (SNR) is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound (CRLB) accuracy for both near-field and far-field sources.
基金Supported by the NNSF of China(11071041)Supported by the Fujian Natural Science Foundation(2009J01002)Supported by the Fujian Department of Education Foundation(JA11270)
文摘The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.
文摘Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.
文摘In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.
基金Foundation item: Supported by the National Science Foundation of China(10701066) Supported by the National Foundation of the Education Department of Henan Province(2008A110022)
文摘A conic Newton method is attractive because it converges to a local minimizzer rapidly from any sufficiently good initial guess. However, it may be expensive to solve the conic Newton equation at each iterate. In this paper we consider an inexact conic Newton method, which solves the couic Newton equation oldy approximately and in sonm unspecified manner. Furthermore, we show that such method is locally convergent and characterizes the order of convergence in terms of the rate of convergence of the relative residuals.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrural Science Foundation.
文摘In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.
文摘Multi-train modeling and simulation plays a vital role in railway electrification during operation and planning phase. Study of peak power demand and energy consumed by each traction substation needs to be deter- mined to verify that electrical energy flowing in its railway power feeding system is appropriate or not. Gauss-Seidel, conventional Newton-Raphson, and current injection methods are well-known and widely accepted as a tool for electrical power network solver in DC railway power supply study. In this paper, a simplified Newton-Raphson method has been proposed. The proposed method employs a set of current-balance equations at each electrical node instead of the conventional power-balance equation used in the conventional Newton-Raphson method. This concept can remarkably reduce execution time and computing complexity for multi-train simulation. To evaluate its use, Sukhumvit line of Bangkok transit system (BTS) of Thai- land with 21.6-km line length and 22 passenger stopping stations is set as a test system. The multi-train simulation integrated with the proposed power network solver is developed to simulate 1-h operation service of selected 5-min headway. From the obtained results, the proposed method is more efficient with approximately 18 % faster than the conventional Newton-Raphson method and just over 6 % faster than the current injection method.