A new blind method is proposed for identification of CDMA Time-Varying (TV)channels in this paper. By representing the TV channel's impulse responses in the delay-Doppler spread domain, the discrete-time canonical...A new blind method is proposed for identification of CDMA Time-Varying (TV)channels in this paper. By representing the TV channel's impulse responses in the delay-Doppler spread domain, the discrete-time canonical model of CDMA-TV systems is developed and a subspace method to identify blindly the Time-Invariant (TI) coordinates is proposed. Unlike existing basis expansion methods, this new algorithm does not require .estimation of the base frequencies, neither need the assumption of linearly varying delays across symbols. The algorithm offers definite explanation of the expansion coordinates. Simulation demonstrates the effectiveness of the algorithm.展开更多
In this study,a one-dimensional two-phase flow four-equation model was developed to simulate the water faucet problem.The performance of six different Krylov subspace methods,namely the generalized minimal residual(GM...In this study,a one-dimensional two-phase flow four-equation model was developed to simulate the water faucet problem.The performance of six different Krylov subspace methods,namely the generalized minimal residual(GMRES),transpose-free quasi-minimal residual,quasi-minimal residual,conjugate gradient squared,biconjugate gradient stabilized,and biconjugate gradient,was evaluated with and without the application of an incomplete LU(ILU)factorization preconditioner for solving the water faucet problem.The simulation results indicate that using the ILU preconditioner with the Krylov subspace methods produces better convergence performance than that without the ILU preconditioner.Only the GMRES demonstrated an acceptable convergence performance under the Krylov subspace methods without the preconditioner.The velocity and pressure distribution in the water faucet problem could be determined using the Krylov subspace methods with an ILU preconditioner,while GMRES could determine it without the need for a preconditioner.However,there are significant advantages of using an ILU preconditioner with the GMRES in terms of efficiency.The different Krylov subspace methods showed similar performance in terms of computational efficiency under the application of the ILU preconditioner.展开更多
A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this...A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.展开更多
The efficiency of three Krylov subspace methods with their ILU0-preconditioned version in solving the systems with the nonadiagonal sparse matrix is examined.The systems have arisen from the discretization of Poisson&...The efficiency of three Krylov subspace methods with their ILU0-preconditioned version in solving the systems with the nonadiagonal sparse matrix is examined.The systems have arisen from the discretization of Poisson's equation using the 4th and 6th-order compact schemes.Four matrix-vector multiplication techniques based on four sparse matrix storage schemes are considered in the algorithm of the Krylov subspace methods and their effects are explored.The convergence history,error reduction,iteration-resolution relation and CPU-time are addressed.The efficacy of various methods is evaluated against a benchmark scenario in which the conventional second-order central difference scheme is employed to discretize Poisson's equation.The Krylov subspace methods,paired with four distinct matrix-vector multiplication strategies across three discretization approaches,are tested and implemented within an incompressible fluid flow solver to solve the elliptic segment of the equations.The resulting solution process CPU-time surface gives a new vision regarding speeding up a CFD code with proper selection of discretization stencil and matrixvector multiplication technique.展开更多
Estimating low-frequency oscillation modes and the corresponding mode shapes based on ambient data from WAMS measurements has a promising prospect in power system analysis and control.Based on the stochastic subspace ...Estimating low-frequency oscillation modes and the corresponding mode shapes based on ambient data from WAMS measurements has a promising prospect in power system analysis and control.Based on the stochastic subspace method,this paper proposes a revised stochastic subspace method by introducing reference channels,which can estimate the modes and the mode shapes simultaneously with great computational efficiency.Meanwhile,the accuracy of the estimated results is not degraded.To discriminate the real modes from the spurious ones,the stabilization diagram is introduced.A novel algorithm is designed to deal with the stabilization diagram which can detect the real modes automatically.Tests conducted on the IEEE-118 system indicate that the proposed method has good performance in terms of both computational efficiency and accuracy,and has the potential of being used on-line.展开更多
A subspace-based blind channel estination algo rithm for MIMO-OFDM systems is proposed. This algorithm exploits the cyclostationarity introduced by cyclic prefix of OFDM to estimate the channel parameters. The propose...A subspace-based blind channel estination algo rithm for MIMO-OFDM systems is proposed. This algorithm exploits the cyclostationarity introduced by cyclic prefix of OFDM to estimate the channel parameters. The proposed new algorithm is found to be outperforming the other algorithm with respect to convergence rate and achievable mean square error and robustness to channel order over determination.展开更多
Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified...Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H-m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo-Elimination method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are further presented.展开更多
In full waveform inversion(FWI)high-resolution subsurface model param-eters are sought.FWI is normally treated as a nonlinear least-squares inverse problem,in which the minimum of the corresponding misfit function is ...In full waveform inversion(FWI)high-resolution subsurface model param-eters are sought.FWI is normally treated as a nonlinear least-squares inverse problem,in which the minimum of the corresponding misfit function is found by updating the model parameters.When multiple elastic or acoustic properties are solved for,simple gradient methods tend to confuse parameter classes.This is referred to as parameter cross-talk;it leads to incorrect model solutions,poor convergence and strong dependence on the scaling of the different parameter types.Determining step lengths in a subspace domain,rather than directly in terms of gradients of different parameters,is a potentially valuable approach to address this problem.The particular subspace used can be defined over a span of different sets of data or different parameter classes,provided it involves a small number of vectors compared to those contained in the whole model space.In a subspace method,the basis vectors are defined first,and a local min-imum is found in the space spanned by these.We examine the application of the sub-space method within acoustic FWI in determining simultaneously updates for velocity and density.We first discuss the choice of basis vectors to construct the spanned space,from linear updates by distinguishing only the contributions of different parameter classes towards nonlinear updates by adding the contributions of higher-order pertur-bations of each parameter class.The numerical character of FWI solutions generated via subspace methods involving different basis vectors is then analyzed and compared with traditional FWI methods.The subspace methods can provide better reconstructions of the model,especially for the velocity,as well as improved convergence rates,while the computational costs are still comparable with the traditional FWI methods.展开更多
We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a ...We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.展开更多
An improved covariance driven subspace identification method is presented to identify the weakly excited modes. In this method, the traditional Hankel matrix is replaced by a reformed one to enhance the identifiabilit...An improved covariance driven subspace identification method is presented to identify the weakly excited modes. In this method, the traditional Hankel matrix is replaced by a reformed one to enhance the identifiability of weak characteristics. The robustness of eigenparameter estimation to noise contamination is reinforced by the improved Hankel matrix, in combination with component energy index （CEI） which indicates the vibration intensity of signal components, an alternative stabilization diagram is adopted to effectively separate spurious and physical modes. Simulation of a vibration system of multiple-degree-of-freedom and experiment of a frame structure subject to wind excitation are presented to demonstrate the improvement of the proposed blind method. The performance of this blind method is assessed in terms of its capability in extracting the weak modes as well as the accuracy of estimated parameters. The results have shown that the proposed blind method gives a better estimation of the weak modes from response signals of small signal to noise ratio （SNR）and gives a reliable separation of spurious and physical estimates.展开更多
The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension ar...The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite展开更多
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua...In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.展开更多
An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution o...An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.展开更多
We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identi...We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identification.The generalized Poisson moment functional is focused.A total least squares equation based on this filtering approach is derived.Inspired by the idea of discrete-time subspace identification based on principal component analysis,we develop two algorithms to deliver consistent estimates for the continuous-time errors-in-variables model by introducing two different instrumental variables.Order determination and other instrumental variables are discussed.The usefulness of the proposed algorithms is illustrated through numerical simulation.展开更多
In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the...In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.展开更多
In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element...In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented subspace.Theoretical analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid,but the computational cost required by the former solution is much lower than that demanded by the latter.The augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L^(2)(Ω)norm compared with the two-scale finite element method.展开更多
Considering the multivariable and fractional-order characteristics of proton exchange membrane fuel cells(PEMFCs),a fractional-order subspace identification method(FOSIM)is proposed in this paper to establish a fracti...Considering the multivariable and fractional-order characteristics of proton exchange membrane fuel cells(PEMFCs),a fractional-order subspace identification method(FOSIM)is proposed in this paper to establish a fractionalorder state space(FOSS)model,which can be expressed as a multivariable configuration with two inputs,hydrogenflow rate and stack current,and two outputs,cell voltage and power.Based on this model,a novel constrained optimal control law named the Hildreth model predictive control(H-MPC)strategy is created,which employs a Hildreth quadratic programming algorithm to adjust the output power of fuel cells through adaptively regulating hydrogen flow and stack current.dSPACE semi-physical simulation results demonstrate that,compared with proportional-integral-derivative and quadratic programming MPC(QP-MPC),the proposed H-MPC exhibits better tracking ability and strong robustness against variations of PEMFC power.展开更多
The letter presents an improved two-dimensional linear discriminant analysis method for feature extraction. Compared with the current two-dimensional methods for feature extraction, the improved two-dimensional linear...The letter presents an improved two-dimensional linear discriminant analysis method for feature extraction. Compared with the current two-dimensional methods for feature extraction, the improved two-dimensional linear discriminant analysis method makes full use of not only the row and the column direc-tion information of face images but also the discriminant information among different classes. The method is evaluated using the Nanjing University of Science and Technology (NUST) 603 face database and the Aleix Martinez and Robert Benavente (AR) face database. Experimental results show that the method in the letter is feasible and effective.展开更多
Vertical layered space-time codes have demonstrated the enormous potential to accommodate rapid flow data. Thus far, vertical layered space-time codes assumed that perfect estimates of current channel fading condition...Vertical layered space-time codes have demonstrated the enormous potential to accommodate rapid flow data. Thus far, vertical layered space-time codes assumed that perfect estimates of current channel fading conditions are available at the receiver. However, increasing the number of transmit antennas increases the required training interval and reduces the available time in which data may be transmitted before the fading coefficients change. In this paper, a vertical layered space-time code is proposed. By applying the subspace method to the layered space-time code, the symbols can be detected without training symbols and channel estimates at the transmitter or the receiver. Monte Carlo simulations show that performance can approach that of the detection method with the knowledge of the channel.展开更多
It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block...It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.展开更多
文摘A new blind method is proposed for identification of CDMA Time-Varying (TV)channels in this paper. By representing the TV channel's impulse responses in the delay-Doppler spread domain, the discrete-time canonical model of CDMA-TV systems is developed and a subspace method to identify blindly the Time-Invariant (TI) coordinates is proposed. Unlike existing basis expansion methods, this new algorithm does not require .estimation of the base frequencies, neither need the assumption of linearly varying delays across symbols. The algorithm offers definite explanation of the expansion coordinates. Simulation demonstrates the effectiveness of the algorithm.
文摘In this study,a one-dimensional two-phase flow four-equation model was developed to simulate the water faucet problem.The performance of six different Krylov subspace methods,namely the generalized minimal residual(GMRES),transpose-free quasi-minimal residual,quasi-minimal residual,conjugate gradient squared,biconjugate gradient stabilized,and biconjugate gradient,was evaluated with and without the application of an incomplete LU(ILU)factorization preconditioner for solving the water faucet problem.The simulation results indicate that using the ILU preconditioner with the Krylov subspace methods produces better convergence performance than that without the ILU preconditioner.Only the GMRES demonstrated an acceptable convergence performance under the Krylov subspace methods without the preconditioner.The velocity and pressure distribution in the water faucet problem could be determined using the Krylov subspace methods with an ILU preconditioner,while GMRES could determine it without the need for a preconditioner.However,there are significant advantages of using an ILU preconditioner with the GMRES in terms of efficiency.The different Krylov subspace methods showed similar performance in terms of computational efficiency under the application of the ILU preconditioner.
文摘A brain tumor occurs when abnormal cells grow, sometimes very rapidly, into an abnormal mass of tissue. The tumor can infect normal tissue, so there is an interaction between healthy and infected cell. The aim of this paper is to propose some efficient and accurate numerical methods for the computational solution of one-dimensional continuous basic models for the growth and control of brain tumors. After computing the analytical solution, we construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization. Then, we investigate the convergence behavior of Conjugate gradient and generalized minimum residual as Krylov subspace methods to solve the tridiagonal toeplitz matrix system derived.
文摘The efficiency of three Krylov subspace methods with their ILU0-preconditioned version in solving the systems with the nonadiagonal sparse matrix is examined.The systems have arisen from the discretization of Poisson's equation using the 4th and 6th-order compact schemes.Four matrix-vector multiplication techniques based on four sparse matrix storage schemes are considered in the algorithm of the Krylov subspace methods and their effects are explored.The convergence history,error reduction,iteration-resolution relation and CPU-time are addressed.The efficacy of various methods is evaluated against a benchmark scenario in which the conventional second-order central difference scheme is employed to discretize Poisson's equation.The Krylov subspace methods,paired with four distinct matrix-vector multiplication strategies across three discretization approaches,are tested and implemented within an incompressible fluid flow solver to solve the elliptic segment of the equations.The resulting solution process CPU-time surface gives a new vision regarding speeding up a CFD code with proper selection of discretization stencil and matrixvector multiplication technique.
基金supported by the National Natural Science Foundation of China (Grant No. 51177079)the Program for Century Excellent Talents in University of China (Grant No. NCET-028-0317)
文摘Estimating low-frequency oscillation modes and the corresponding mode shapes based on ambient data from WAMS measurements has a promising prospect in power system analysis and control.Based on the stochastic subspace method,this paper proposes a revised stochastic subspace method by introducing reference channels,which can estimate the modes and the mode shapes simultaneously with great computational efficiency.Meanwhile,the accuracy of the estimated results is not degraded.To discriminate the real modes from the spurious ones,the stabilization diagram is introduced.A novel algorithm is designed to deal with the stabilization diagram which can detect the real modes automatically.Tests conducted on the IEEE-118 system indicate that the proposed method has good performance in terms of both computational efficiency and accuracy,and has the potential of being used on-line.
基金Supported by the Scientific Development Fund of Shanghai Scientific Committee(037062022)
文摘A subspace-based blind channel estination algo rithm for MIMO-OFDM systems is proposed. This algorithm exploits the cyclostationarity introduced by cyclic prefix of OFDM to estimate the channel parameters. The proposed new algorithm is found to be outperforming the other algorithm with respect to convergence rate and achievable mean square error and robustness to channel order over determination.
文摘Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H-m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo-Elimination method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are further presented.
文摘In full waveform inversion(FWI)high-resolution subsurface model param-eters are sought.FWI is normally treated as a nonlinear least-squares inverse problem,in which the minimum of the corresponding misfit function is found by updating the model parameters.When multiple elastic or acoustic properties are solved for,simple gradient methods tend to confuse parameter classes.This is referred to as parameter cross-talk;it leads to incorrect model solutions,poor convergence and strong dependence on the scaling of the different parameter types.Determining step lengths in a subspace domain,rather than directly in terms of gradients of different parameters,is a potentially valuable approach to address this problem.The particular subspace used can be defined over a span of different sets of data or different parameter classes,provided it involves a small number of vectors compared to those contained in the whole model space.In a subspace method,the basis vectors are defined first,and a local min-imum is found in the space spanned by these.We examine the application of the sub-space method within acoustic FWI in determining simultaneously updates for velocity and density.We first discuss the choice of basis vectors to construct the spanned space,from linear updates by distinguishing only the contributions of different parameter classes towards nonlinear updates by adding the contributions of higher-order pertur-bations of each parameter class.The numerical character of FWI solutions generated via subspace methods involving different basis vectors is then analyzed and compared with traditional FWI methods.The subspace methods can provide better reconstructions of the model,especially for the velocity,as well as improved convergence rates,while the computational costs are still comparable with the traditional FWI methods.
文摘We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.
基金This project is supported by National Natural Science Foundation of China (No.10302019).
文摘An improved covariance driven subspace identification method is presented to identify the weakly excited modes. In this method, the traditional Hankel matrix is replaced by a reformed one to enhance the identifiability of weak characteristics. The robustness of eigenparameter estimation to noise contamination is reinforced by the improved Hankel matrix, in combination with component energy index （CEI） which indicates the vibration intensity of signal components, an alternative stabilization diagram is adopted to effectively separate spurious and physical modes. Simulation of a vibration system of multiple-degree-of-freedom and experiment of a frame structure subject to wind excitation are presented to demonstrate the improvement of the proposed blind method. The performance of this blind method is assessed in terms of its capability in extracting the weak modes as well as the accuracy of estimated parameters. The results have shown that the proposed blind method gives a better estimation of the weak modes from response signals of small signal to noise ratio （SNR）and gives a reliable separation of spurious and physical estimates.
基金Project supported by the National Natural Science Foundation of China(Grant No.10926082)the Natural Science Foundation of Anhui Province of China(Grant No.KJ2010A128)the Fund for Youth of Anhui Normal University,China(Grant No.2009xqn55)
文摘The invariant subspace method is used to construct the explicit solution of a nonlinear evolution equation. The second-order nonlinear differential operators that possess invariant subspaces of submaximal dimension are described. There are second-order nonlinear differential operators, including cubic operators and quadratic operators, which preserve an invariant subspace of submaximal dimension. A full. description, of the second-order cubic operators with constant coefficients admitting a four-dimensional invariant subspace is given. It is shown that the maximal dimension of invaxiant subspaces preserved by a second-order cubic operator is four. Several examples are given for the construction of the exact solutions to nonlinear evolution equations with cubic nonlinearities. These solutions blow up in a finite
基金supported by the National Natural Science Foundation of China(Grant No.11371293)the Civil Military Integration Research Foundation of Shaanxi Province,China(Grant No.13JMR13)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Grant No.14JK1246)the Mathematical Discipline Foundation of Shaanxi Province,China(Grant No.14SXZD015)the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)
文摘In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
文摘An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.
基金supported by the National Natural Science Foundation of China (Nos.60674086 and 60736021)the Scientific and Technology Plan of Zhejiang Province,China (No.2007C21173)
文摘We study the subspace identification for the continuous-time errors-in-variables model from sampled data.First,the filtering approach is applied to handle the time-derivative problem inherent in continuous-time identification.The generalized Poisson moment functional is focused.A total least squares equation based on this filtering approach is derived.Inspired by the idea of discrete-time subspace identification based on principal component analysis,we develop two algorithms to deliver consistent estimates for the continuous-time errors-in-variables model by introducing two different instrumental variables.Order determination and other instrumental variables are discussed.The usefulness of the proposed algorithms is illustrated through numerical simulation.
文摘In this paper we reconsider the range-restricted GMRES (RRGMRES) method for solving nonsymmetric linear systems. We first review an important result for the usual GMRES method. Then we give an example to show that the range-restricted GMRES method does not admit such a result. Finally, we give a modified result for the range-restricted GMRES method. We point out that the modified version can be used to show that the range-restricted GMRES method is also a regularization method for solving linear ill-posed problems.
基金supported by the National Key R&D Program of China under Grant Nos.2019YFA0709600 and 2019YFA0709601the National Natural Science Foundation of China under Grant No.12021001+2 种基金supported by the National Natural Science Foundation of China under Grant No.92270206supported by the National Natural Science Foundation of China(Grant No.11771467)the disciplinary funding of Central University of Finance and Economics.
文摘In this paper,an augmented two-scale finite element method is proposed for a class of linear and nonlinear eigenvalue problems on tensor-product domains.Through a correction step,the augmented two-scale finite element solution is obtained by solving an eigenvalue problem on a low-dimensional augmented subspace.Theoretical analysis and numerical experiments show that the augmented two-scale finite element solution achieves the same order of accuracy as the standard finite element solution on a fine grid,but the computational cost required by the former solution is much lower than that demanded by the latter.The augmented two-scale finite element method also improves the approximation accuracy of eigenfunctions in the L^(2)(Ω)norm compared with the two-scale finite element method.
基金This work was supported in part by National Natural Science Foundation of China grant No.61374153 and grant No.52377209in part by“Postgraduate Research&Practice Innovation Program of Jiangsu Province”(grant No.SJCX23_0132).
文摘Considering the multivariable and fractional-order characteristics of proton exchange membrane fuel cells(PEMFCs),a fractional-order subspace identification method(FOSIM)is proposed in this paper to establish a fractionalorder state space(FOSS)model,which can be expressed as a multivariable configuration with two inputs,hydrogenflow rate and stack current,and two outputs,cell voltage and power.Based on this model,a novel constrained optimal control law named the Hildreth model predictive control(H-MPC)strategy is created,which employs a Hildreth quadratic programming algorithm to adjust the output power of fuel cells through adaptively regulating hydrogen flow and stack current.dSPACE semi-physical simulation results demonstrate that,compared with proportional-integral-derivative and quadratic programming MPC(QP-MPC),the proposed H-MPC exhibits better tracking ability and strong robustness against variations of PEMFC power.
文摘The letter presents an improved two-dimensional linear discriminant analysis method for feature extraction. Compared with the current two-dimensional methods for feature extraction, the improved two-dimensional linear discriminant analysis method makes full use of not only the row and the column direc-tion information of face images but also the discriminant information among different classes. The method is evaluated using the Nanjing University of Science and Technology (NUST) 603 face database and the Aleix Martinez and Robert Benavente (AR) face database. Experimental results show that the method in the letter is feasible and effective.
基金Partially supported by the National Natural Sciences Foundation (No.69872029) and the Research Fund for Doctoral Program of Higher Education (No.1999069808) of China
文摘Vertical layered space-time codes have demonstrated the enormous potential to accommodate rapid flow data. Thus far, vertical layered space-time codes assumed that perfect estimates of current channel fading conditions are available at the receiver. However, increasing the number of transmit antennas increases the required training interval and reduces the available time in which data may be transmitted before the fading coefficients change. In this paper, a vertical layered space-time code is proposed. By applying the subspace method to the layered space-time code, the symbols can be detected without training symbols and channel estimates at the transmitter or the receiver. Monte Carlo simulations show that performance can approach that of the detection method with the knowledge of the channel.
文摘It was proposed that a robust and efficient parallelizable preconditioner for solving general sparse linear systems of equations, in which the use of sparse approximate inverse (AINV) techniques in a multi-level block ILU (BILUM) preconditioner were investigated. The resulting preconditioner retains robustness of BILUM preconditioner and has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.
