There has been an increasing emphasis on performing deep neural network(DNN)inference locally on edge devices due to challenges such as network congestion and security concerns.However,as DRAM process technology conti...There has been an increasing emphasis on performing deep neural network(DNN)inference locally on edge devices due to challenges such as network congestion and security concerns.However,as DRAM process technology continues to scale down,the bit-flip errors in the memory of edge devices become more frequent,thereby leading to substantial DNN inference accuracy loss.Though several techniques have been proposed to alleviate the accuracy loss in edge environments,they require complex computations and additional parity bits for error correction,thus resulting in significant performance and storage overheads.In this paper,we propose FeatherGuard,a data-driven lightweight error protection scheme for DNN inference on edge devices.FeatherGuard selectively protects critical bit positions(that have a significant impact on DNN inference accuracy)against bit-flip errors,by considering various DNN characteristics(e.g.,data format,layer-wise weight distribution,actually stored logical values).Thus,it achieves high error tolerability during DNN inference.Since FeatherGuard reduces the bit-flip errors based on only a few simple arithmetic operations(e.g.,NOT operations)without parity bits,it causes negligible performance overhead and no storage overhead.Our experimental results show that FeatherGuard improves the error tolerability by up to 6667×and 4000×,compared to the conventional systems and the state-of-the-art error protection technique for edge environments,respectively.展开更多
This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administratio...This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.展开更多
AIM:To evaluate the efficacy of the total computer vision syndrome questionnaire(CVS-Q)score as a predictive tool for identifying individuals with symptomatic binocular vision anomalies and refractive errors.METHODS:A...AIM:To evaluate the efficacy of the total computer vision syndrome questionnaire(CVS-Q)score as a predictive tool for identifying individuals with symptomatic binocular vision anomalies and refractive errors.METHODS:A total of 141 healthy computer users underwent comprehensive clinical visual function assessments,including evaluations of refractive errors,accommodation(amplitude of accommodation,positive relative accommodation,negative relative accommodation,accommodative accuracy,and accommodative facility),and vergence(phoria,positive and negative fusional vergence,near point of convergence,and vergence facility).Total CVS-Q scores were recorded to explore potential associations between symptom scores and the aforementioned clinical visual function parameters.RESULTS:The cohort included 54 males(38.3%)with a mean age of 23.9±0.58y and 87 age-matched females(61.7%)with a mean age of 23.9±0.53y.The multiple regression model was statistically significant[R²=0.60,F=13.28,degrees of freedom(DF=17122,P<0.001].This indicates that 60%of the variance in total CVS-Q scores(reflecting reported symptoms)could be explained by four clinical measurements:amplitude of accommodation,positive relative accommodation,exophoria at distance and near,and positive fusional vergence at near.CONCLUSION:The total CVS-Q score is a valid and reliable tool for predicting the presence of various nonstrabismic binocular vision anomalies and refractive errors in symptomatic computer users.展开更多
In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error est...In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.展开更多
A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the...A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.展开更多
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.展开更多
The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satis...The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error...The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error of view and target height. A method is proposed in this paper to estimate the angle error from the return signal. The method makes use of the relationship between the view angle error and the signal correlation of the subswaths to estimate the angle error. The precision of this method is analyzed by the law of great number and it turns out to be in direct proportion to the root square number of averaging. The simulation result is given and the angle precision is 0.025°.展开更多
A rock-drilling jumbo is the main piece of tunneling equipment used in the energy and infrastructure industries in various countries.The positioning accuracy of its drilling boom greatly affects tunneling efficiency a...A rock-drilling jumbo is the main piece of tunneling equipment used in the energy and infrastructure industries in various countries.The positioning accuracy of its drilling boom greatly affects tunneling efficiency and section-forming quality of mine roadways and engineering tunnels.In order to improve the drilling-positioning accuracy of a three-boom drilling jumbo,we established a kinematics model of the multi-degree-of-freedom(multi-DOF)multi-boom system,using the improved Denavit-Hartenberg(D-H)method,and obtained the mapping relationship between the end position and the amount of motion of each joint.The error of the inverse kinematics calculation for the drilling boom is estimated by an analytical method and a global search algorithm based on particle swarm optimization(PSO)for a straight blasting hole and an inclined blasting hole.On this basis,we propose a back-propagation(BP)neural network optimized by an improved sparrow search algorithm(ISSA)to predict the positioning error of the drilling booms of a three-boom drilling jumbo.In order to verify the accuracy of the proposed error compensation model,we built an automatic-control test platform for the boom,and carried out a positioning error compensation test on the boom.The results show that the average drilling-positioning error was reduced from 9.79 to 5.92 cm,and the error was reduced by 39.5%.Therefore,the proposed method effectively reduces the positioning error of the drilling boom,and improves the accuracy and efficiency of rock drilling.展开更多
Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-v...Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.展开更多
This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator ...This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.展开更多
In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is establ...In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.展开更多
In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimati...In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.展开更多
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.展开更多
Industrial robots are integral to modern manufacturing systems,enabling high precision,high throughput,and flexibility.However,errors in accuracy and repeatability,which arise from a variety of sources such as mechani...Industrial robots are integral to modern manufacturing systems,enabling high precision,high throughput,and flexibility.However,errors in accuracy and repeatability,which arise from a variety of sources such as mechanical wear,calibration issues,and environmental factors,can significantly impact the performance of industrial robots.This paper aims to explore the theoretical modeling of errors in industrial robot systems and propose compensation strategies to enhance their accuracy and repeatability.Key factors contributing to errors,such as kinematic,dynamic,and environmental influences,are discussed in detail.Additionally,the paper explores various compensation techniques,including geometric error compensation,dynamic compensation,and adaptive control approaches.Through the integration of error modeling and compensation methods,industrial robots can achieve improved performance,ensuring higher operational efficiency and product quality.The paper concludes by highlighting the challenges and future research directions for improving the accuracy and repeatability of industrial robots in practical applications.展开更多
Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level met...Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.展开更多
A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presen...A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.展开更多
In this paper,the uniform error estimates with respect to t∈[0, ∞ ) of the nonlinear Galerkin method are given for the long time integration of the Kuramoto-Sivashinsky equation. The nonlinear Galerkin method is use...In this paper,the uniform error estimates with respect to t∈[0, ∞ ) of the nonlinear Galerkin method are given for the long time integration of the Kuramoto-Sivashinsky equation. The nonlinear Galerkin method is used to study the asymptotic behaviour of Kuramoto-Sivashinsky equation and to construct the bifurcation diagrams.展开更多
In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci s...In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.展开更多
基金the“Convergence and Open sharing System”Project,supported by the Ministry of Education and National Research Foundation of Korea.
文摘There has been an increasing emphasis on performing deep neural network(DNN)inference locally on edge devices due to challenges such as network congestion and security concerns.However,as DRAM process technology continues to scale down,the bit-flip errors in the memory of edge devices become more frequent,thereby leading to substantial DNN inference accuracy loss.Though several techniques have been proposed to alleviate the accuracy loss in edge environments,they require complex computations and additional parity bits for error correction,thus resulting in significant performance and storage overheads.In this paper,we propose FeatherGuard,a data-driven lightweight error protection scheme for DNN inference on edge devices.FeatherGuard selectively protects critical bit positions(that have a significant impact on DNN inference accuracy)against bit-flip errors,by considering various DNN characteristics(e.g.,data format,layer-wise weight distribution,actually stored logical values).Thus,it achieves high error tolerability during DNN inference.Since FeatherGuard reduces the bit-flip errors based on only a few simple arithmetic operations(e.g.,NOT operations)without parity bits,it causes negligible performance overhead and no storage overhead.Our experimental results show that FeatherGuard improves the error tolerability by up to 6667×and 4000×,compared to the conventional systems and the state-of-the-art error protection technique for edge environments,respectively.
基金supported by the National Key R&D Program of China [grant number 2023YFC3008004]。
文摘This study presents a comprehensive evaluation of tropical cyclone(TC)forecast performance in the western North Pacific from 2013 to 2022,based on operational forecasts issued by the China Meteorological Administration.The analysis reveals systematic improvements in both track and intensity forecasts over the decade,with distinct error characteristics observed across various forecast parameters.Track forecast errors have steadily decreased,particularly for longer lead times,while error magnitudes have increased with longer forecast lead times.Intensity forecasts show similar progressive enhancements,with maximum sustained wind speed errors decreasing by 0.26 m/s per year for 120 h forecasts.The study also identifies several key patterns in forecast performance:typhoon-grade or stronger TCs exhibit smaller track errors than week or weaker systems;intensity forecasts systematically overestimate weaker TCs while underestimating stronger systems;and spatial error distributions show greater track inaccuracies near landmasses and regional intensity biases.These findings highlight both the significant advances in TC forecasting capability achieved through improved modeling and observational systems,and the remaining challenges in predicting TC changes and landfall behavior,providing valuable benchmarks for future forecast system development.
基金Supported by Ongoing Research Funding Program(ORFFT-2025-054-1),King Saud University,Riyadh,Saudi Arabia.
文摘AIM:To evaluate the efficacy of the total computer vision syndrome questionnaire(CVS-Q)score as a predictive tool for identifying individuals with symptomatic binocular vision anomalies and refractive errors.METHODS:A total of 141 healthy computer users underwent comprehensive clinical visual function assessments,including evaluations of refractive errors,accommodation(amplitude of accommodation,positive relative accommodation,negative relative accommodation,accommodative accuracy,and accommodative facility),and vergence(phoria,positive and negative fusional vergence,near point of convergence,and vergence facility).Total CVS-Q scores were recorded to explore potential associations between symptom scores and the aforementioned clinical visual function parameters.RESULTS:The cohort included 54 males(38.3%)with a mean age of 23.9±0.58y and 87 age-matched females(61.7%)with a mean age of 23.9±0.53y.The multiple regression model was statistically significant[R²=0.60,F=13.28,degrees of freedom(DF=17122,P<0.001].This indicates that 60%of the variance in total CVS-Q scores(reflecting reported symptoms)could be explained by four clinical measurements:amplitude of accommodation,positive relative accommodation,exophoria at distance and near,and positive fusional vergence at near.CONCLUSION:The total CVS-Q score is a valid and reliable tool for predicting the presence of various nonstrabismic binocular vision anomalies and refractive errors in symptomatic computer users.
基金supported by National Natural Science Foundation of China (11071226 11201122)
文摘In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.
基金The research was supported by the Natural Science Foundation of China
文摘A nonlinear parabolic system is derived to describe incompressible nuclear waste-disposal contamination in porous media. A sequential implicit tirne-stepping is defined, in which the pressure and Darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the brine, radionuclid and heat are treated by a combination of a Galerkin finite element method and the method of characteristics. Optimal-order convergence in L2 is proved. Time-truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the brine, radionuclide and heal equalios, temporal and spatial error are lossened by direct compulation of the velocity in the mixed method, as opposed to differentiation of the pressure.
基金Supported by NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
基金the Henan Natural Science Foundation(072300410320)the Henan Education Department Foundational Study Foundation(200510460311)
文摘The main aim of this paper is to have an accurate analysis on the famous Adini＇s element for the second order problems under to the anisotropic meshes. We firstly show that the interpolation of Adini＇s element satisfy the anisotropic property. Then the optimal error estimate is obtained without the regularity assumption on the meshes.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
文摘The wide-swath method based on multi-receiver is a novel and highly accurate wide-swath method, which requires a very precise view angle. The estimated angle has error because of the atmosphere refraction, angle error of view and target height. A method is proposed in this paper to estimate the angle error from the return signal. The method makes use of the relationship between the view angle error and the signal correlation of the subswaths to estimate the angle error. The precision of this method is analyzed by the law of great number and it turns out to be in direct proportion to the root square number of averaging. The simulation result is given and the angle precision is 0.025°.
基金National Natural Science Foundation of China(No.12472038)Natural Science Foundation of Jiangsu Province(No.BK20230688)+2 种基金Natural Science Foundation of the Jiangsu Higher Education Institutions of China(No.22KJB440004)Key Research and Development Program of Xuzhou(No.KC22404)Research Fund for Doctoral Degree Teachers of Jiangsu Normal University of China(No.22XFRS011).
文摘A rock-drilling jumbo is the main piece of tunneling equipment used in the energy and infrastructure industries in various countries.The positioning accuracy of its drilling boom greatly affects tunneling efficiency and section-forming quality of mine roadways and engineering tunnels.In order to improve the drilling-positioning accuracy of a three-boom drilling jumbo,we established a kinematics model of the multi-degree-of-freedom(multi-DOF)multi-boom system,using the improved Denavit-Hartenberg(D-H)method,and obtained the mapping relationship between the end position and the amount of motion of each joint.The error of the inverse kinematics calculation for the drilling boom is estimated by an analytical method and a global search algorithm based on particle swarm optimization(PSO)for a straight blasting hole and an inclined blasting hole.On this basis,we propose a back-propagation(BP)neural network optimized by an improved sparrow search algorithm(ISSA)to predict the positioning error of the drilling booms of a three-boom drilling jumbo.In order to verify the accuracy of the proposed error compensation model,we built an automatic-control test platform for the boom,and carried out a positioning error compensation test on the boom.The results show that the average drilling-positioning error was reduced from 9.79 to 5.92 cm,and the error was reduced by 39.5%.Therefore,the proposed method effectively reduces the positioning error of the drilling boom,and improves the accuracy and efficiency of rock drilling.
基金Supported by National Natural Science Foundation of China(Grant Nos.52375018,92148301).
文摘Contour error is the deviation between the actual displacement and reference trajectory,which is directly related to the machining accuracy.Contour error compensation poses substantial challenges because of the time-varying,nonlinear,and strongly coupled characteristics of parallel machining modules.In addition,the time delay in the system reduces the timeliness of the feedback data,thereby making online contour error calculations and compensation particularly difficult.To solve this problem,the generation mechanism of the time delay of the feedback data and contour error is revealed,and a systematic method for the identification of the time-delay parameter based on Beckhoff’s tracking error calculation mechanism is proposed.The temporal alignment between the position commands and feedback data enables the online calculation of the contour error.On this basis,the tracking error of the drive axes(an important factor resulting in end-effector contour errors)is used for the contour error calculation.Considering the ambiguous parameter-setting logic of the servo drive,the servo parameter is calculated in reverse using the steady-state error to obtain the tracking error model of the drive axes.Furthermore,combined with the system time-delay model,an online correction method for the tracking error estimation model is established.To achieve an accurate mapping of the drive-axis tracking error and end-effector contour error,a bounded iterative search method for the nearest contour point and online calculation model for the contour error are respectively established.Finally,an online compensation controller for contour error is designed.Its effectiveness is verified by a machining experiment on a frame workpiece.The machining results show that the contour error reduces from 68μm to 45μm,and the finish machining accuracy increases by 34%.This study provides a feasible method for online compensation of contour error in a system with time delay.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1236108412001130)。
文摘This paper is devoted to the Polynomial Preserving Recovery (PPR) based a posteriori error analysis for the second-order elliptic non-symmetric eigenvalue problem. An asymptotically exact a posteriori error estimator is proposed for solving the convection-dominated non-symmetric eigenvalue problem with non-smooth eigenfunctions or multiple eigenvalues. Numerical examples confirm our theoretical analysis.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrual Science Foundation.
文摘In this paper we give an almost sharp error estimate of Halley’s iteration for the majorizing sequence. Compared with the corresponding results in [6,14], it is far better. Meanwhile,the convergence theorem is established .for Halley’s iteration in Banach spaces.
文摘In this paper, a spectral method to analyze the generalized Benjamin Bona Mahony equations is used. The existence and uniqueness of global smooth solution of these equations are proved. The large time error estimation between the spectral approximate solution and the exact solution is obtained.
文摘A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
文摘Industrial robots are integral to modern manufacturing systems,enabling high precision,high throughput,and flexibility.However,errors in accuracy and repeatability,which arise from a variety of sources such as mechanical wear,calibration issues,and environmental factors,can significantly impact the performance of industrial robots.This paper aims to explore the theoretical modeling of errors in industrial robot systems and propose compensation strategies to enhance their accuracy and repeatability.Key factors contributing to errors,such as kinematic,dynamic,and environmental influences,are discussed in detail.Additionally,the paper explores various compensation techniques,including geometric error compensation,dynamic compensation,and adaptive control approaches.Through the integration of error modeling and compensation methods,industrial robots can achieve improved performance,ensuring higher operational efficiency and product quality.The paper concludes by highlighting the challenges and future research directions for improving the accuracy and repeatability of industrial robots in practical applications.
文摘Residual based on a posteriori error estimates for conforming finite element solutions of incompressible Navier-Stokes equations with stream function form which were computed with seven recently proposed two-level method were derived. The posteriori error estimates contained additional terms in comparison to the error estimates for the solution obtained by the standard finite element method. The importance of these additional terms in the error estimates was investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than of convergence of discrete solution.
基金Project supported by the National Natural Science Foundation of China (No. 60874039)Shanghai Leading Academic Discipline Project (No. J50101)
文摘A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.
文摘In this paper,the uniform error estimates with respect to t∈[0, ∞ ) of the nonlinear Galerkin method are given for the long time integration of the Kuramoto-Sivashinsky equation. The nonlinear Galerkin method is used to study the asymptotic behaviour of Kuramoto-Sivashinsky equation and to construct the bifurcation diagrams.
基金Supported by NSFC(Nos.12371051,12141101,11871126)。
文摘In this paper,we study and characterize the volume estimates of geodesic balls on Finsler gradient Ricci solitons.We get the upper bounds on the volumes of geodesic balls of all three kinds of Finsler gradient Ricci solitons under certain condition about the Laplacian of thedistance function.
