Since language is a tool for communication,proficiency in English communication is a fundamental necessity for talent in the 21st century.However,surveys reveal that most college students at private colleges possess i...Since language is a tool for communication,proficiency in English communication is a fundamental necessity for talent in the 21st century.However,surveys reveal that most college students at private colleges possess inadequate oral English skills,and what some have learned is“mute English.”Therefore,developing their English-speaking skills is another challenge faced by students attending private schools.Online diagnostic assessment methods are growing globally with the use of technology.UDig diagnostic assessment system is one of the online English diagnostic assessment platforms currently being widely used in China.Therefore,the present work is conducted to investigate and conduct an oral English learning-oriented assessment model in college English using the online diagnostic assessment.With the research result,it is hoped that the study could provide useful information for improving UDig system and make a better use of it in college oral English learning and teaching.展开更多
A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum sol...A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.展开更多
A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of ...A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated. [ABSTRACT FROM AUTHOR]展开更多
We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about...We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.展开更多
We derive new and tight bounds about the eigenvalues and certain sums of the eigenvalues for the unique symmetric positive definite solutions of the discrete algebraic Riccati equations. These bounds considerably impr...We derive new and tight bounds about the eigenvalues and certain sums of the eigenvalues for the unique symmetric positive definite solutions of the discrete algebraic Riccati equations. These bounds considerably improve the existing ones and treat the cases that have been not discussed in the literature. Besides, they also result in completions for the available bounds about the extremal eigenvalues and the traces of the solutions of the discrete algebraic Riccati equations. We study the fixed-point iteration methods for com- puting the symmetric positive definite solutions of the discrete algebraic Riccati equations and establish their general convergence theory. By making use of the Schulz iteration to partially avoid computing the matrix inversions, we present effective variants of the fixed-point iterations, prove their monotone convergence and estimate their asymptotic convergence rates. Numerical results show that the modified fixed-point iteration methods are feasible and effective solvers for computing the symmetric positive definite solutions of the discrete algebraic Riccati equations.展开更多
Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared （CORS） method is often competitive with other popular methods. However, the CORS method, l...Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared （CORS） method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irreg- ular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the bicon- jugate A-orthogonal residual （BiCOR） method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.展开更多
文摘Since language is a tool for communication,proficiency in English communication is a fundamental necessity for talent in the 21st century.However,surveys reveal that most college students at private colleges possess inadequate oral English skills,and what some have learned is“mute English.”Therefore,developing their English-speaking skills is another challenge faced by students attending private schools.Online diagnostic assessment methods are growing globally with the use of technology.UDig diagnostic assessment system is one of the online English diagnostic assessment platforms currently being widely used in China.Therefore,the present work is conducted to investigate and conduct an oral English learning-oriented assessment model in college English using the online diagnostic assessment.With the research result,it is hoped that the study could provide useful information for improving UDig system and make a better use of it in college oral English learning and teaching.
基金This research is partially supported by the National Natural Science Foundation of China (No. 10271055).
文摘A kind of inverse eigenvalue problem in structural dynamics design is considered. The problem is formulated as an optimization problem. The properties of this problem are analyzed, and the existence of the optimum solution is proved. The directional derivative of the objective function is obtained and a necessary condition for a point to be a local minimum point is given. Then a numerical algorithm for solving the problem is presented and a plane-truss problem is discussed to show the applications of the theories and the algorithm.
基金National Natural Science Foundation of ChinaJiangsu Province Natural Science FoundationJiangsu Province "333 Engineering
文摘A preconditioned iterative method for computing a few eigenpairs of large sparse symmetric matrices is presented in this paper. The proposed method which combines the preconditioning techniques with the efficiency of block Lanczos algorithm is suitable for determination of the extreme eigenvalues as well as their multiplicities. The global convergence and the asymptotically quadratic convergence of the new method are also demonstrated. [ABSTRACT FROM AUTHOR]
基金supported by the National Basic Research Program(No.2005CB321702)the China Outstanding Young Scientist F0undation(No.10525102)the National Natural Science Foundation (No.10471146),P.R.China
文摘We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.
基金Acknowledgments. This work was started when the first author was visiting State Key Laboratory of Scientific/Engineering Computing, Chinese Academy of Sciences, during March-May in 2008. The support and hospitality from LSEC are very much appreciated. Supported by The National Basic Research Program （No. 2005CB321702）, The China Outstanding Young Scientist Foundation （No. 10525102）, and The National Natural Science Foundation for Innovative Research Groups （No. 11021101）, P.R. China.
文摘We derive new and tight bounds about the eigenvalues and certain sums of the eigenvalues for the unique symmetric positive definite solutions of the discrete algebraic Riccati equations. These bounds considerably improve the existing ones and treat the cases that have been not discussed in the literature. Besides, they also result in completions for the available bounds about the extremal eigenvalues and the traces of the solutions of the discrete algebraic Riccati equations. We study the fixed-point iteration methods for com- puting the symmetric positive definite solutions of the discrete algebraic Riccati equations and establish their general convergence theory. By making use of the Schulz iteration to partially avoid computing the matrix inversions, we present effective variants of the fixed-point iterations, prove their monotone convergence and estimate their asymptotic convergence rates. Numerical results show that the modified fixed-point iteration methods are feasible and effective solvers for computing the symmetric positive definite solutions of the discrete algebraic Riccati equations.
基金The authors are grateful to the referees for their valuable comments and suggestions which helped to improve the presentation of this paper. The research is supported by the National Natural Science Foundation of China under grant No.11071118, Natural Science Foundation from Anhui Province Education Department under grant No.KJ2012B058 and AHSTU under grant No.ZRC2013388.
文摘Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared （CORS） method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irreg- ular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the bicon- jugate A-orthogonal residual （BiCOR） method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.
