In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp...The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.展开更多
Iterative Learning Control(ILC)provides an effective framework for optimizing repetitive tasks,making it particularly suitable for high-precision applications in both precision manufacturing and intelligent transporta...Iterative Learning Control(ILC)provides an effective framework for optimizing repetitive tasks,making it particularly suitable for high-precision applications in both precision manufacturing and intelligent transportation systems(ITS).This paper presents a systematic review of ILC's developmental progress,current methodologies,and practical implementations across these two critical domains.The review first analyzes the key technical challenges encountered when integrating ILC into precision manufacturing workflows.Through case studies,it evaluates demonstrated improvements in positioning accuracy,surface finish quality,and production throughput.Furthermore,the study examines ILC’s applications in ITS,with particular focus on vehicular motion control applications including autonomous vehicle trajectory tracking,platoon coordination,and traffic signal timing optimization,where its data-driven characteristics enhance adaptability to dynamic environments.Finally,the paper proposes targeted future research directions that are essential for fully realizing ILC’s potential in advancing these interconnected yet distinct fields.展开更多
The iterative continuation task(ICT)requires English as a foreign language(EFL)learners to read a segment and write a continuation that aligns with the preceding segment of an English novel with successive turns,offer...The iterative continuation task(ICT)requires English as a foreign language(EFL)learners to read a segment and write a continuation that aligns with the preceding segment of an English novel with successive turns,offering exposure to diverse grammatical structures and opportunities for contextualized usage.Given the importance of integrating technology into second language(L2)writing and the critical role that grammar plays in L2 writing development,automated written corrective feedback provided by Grammarly has gained significant attention.This study investigates the impact of Grammarly on grammar learning strategies,grammar grit,and grammar competence among EFL college students engaged in ICT.This study employed a mixed-methods sequential exploratory design;56 participants were divided into an experimental group(n=28),receiving Grammarly feedback for ICT,and a control group(n=28),completing ICT without Grammarly feedback.Quantitative results revealed that both groups showed improvements in L2 grammar learning strategies,grit and competence.For the experimental group,significant differences were observed across all variables of L2 grammar learning strategies,grit,and competence between pre-and post-tests.For the control group,significant differences were only observed in the affective dimension of grammar learning strategies,Consistency of Interest(COI)of grammar grit,and grammar competence.However,the control group presented a significantly higher improvement in grammar competence.Qualitative analysis showed both positive and negative perceptions of Grammarly.The pedagogical implications of integrating Grammarly and ICT for L2 grammar development are discussed.展开更多
Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural ...Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.展开更多
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for...An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.展开更多
In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduce...In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.展开更多
In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.
Under the weak Lipschitz condition about the solution of the equation, convergence theorems for a family of iterations with one parameter are obtained. An estimation of the radius of the attraction ball is shown. At l...Under the weak Lipschitz condition about the solution of the equation, convergence theorems for a family of iterations with one parameter are obtained. An estimation of the radius of the attraction ball is shown. At last two examples are given.展开更多
The simultaneous iterations rithms of the ART family. It is used reconstruction technique （SIRT） widely in tomography because of is one of several reconstruction algoits convenience in dealing with large sparse matr...The simultaneous iterations rithms of the ART family. It is used reconstruction technique （SIRT） widely in tomography because of is one of several reconstruction algoits convenience in dealing with large sparse matrices. Its theoretical background and iteration model are discussed at the beginning of this paper. Then, the implementation of the SIRT to reconstruct the three-dimensional distribution of water vapor by simulation is discussed. The results show that the SIRT can function effectively in water vapor tomography, obtain rapid convergence, and be implemented more easily than inversion.展开更多
Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phas...Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.展开更多
This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>&...This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>×<em>n</em> matrix, <em>A</em>. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, <em>G</em>, this method computes<em> k</em> dominant eigenvectors of <em>G</em>. To see the relation between these methods we assume that <em>G </em>=<em> A</em><sup>T</sup> <em>A</em>. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.展开更多
This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two i...This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N｜｜f｜｜-1/v2≤1/√2＋1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.展开更多
A new restoration algorithm based on double loops and alternant iterations is proposed to restore the object image effectively from a few frames of turbulence-degraded images, Based on the double loops, the iterative ...A new restoration algorithm based on double loops and alternant iterations is proposed to restore the object image effectively from a few frames of turbulence-degraded images, Based on the double loops, the iterative relations for estimating the turbulent point spread function PSF and object image alternately are derived. The restoration experiments have been made on computers, showing that the proposed algorithm can obtain the optimal estimations of the object and the point spread function, with the feasibility and practicality of the proposed algorithm being convincing.展开更多
In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods ...In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.展开更多
In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of ...In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.展开更多
We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-st...We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.展开更多
Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the ...Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.展开更多
In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the inte...In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金The National Natural Science Foundations of China (12202219)the Natural Science Foundations of Ningxia (2024AAC02009, 2023AAC05001)the Ningxia Youth Top Talents Training Project。
文摘The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.
基金funded by the Wuxi Young Scientific and Technological Talent Support Initiative,project number:TJXD-2024-203the Natural Science Foundation of the Jiangsu Higher Education Institutions of China,grant number:24KJB470027.
文摘Iterative Learning Control(ILC)provides an effective framework for optimizing repetitive tasks,making it particularly suitable for high-precision applications in both precision manufacturing and intelligent transportation systems(ITS).This paper presents a systematic review of ILC's developmental progress,current methodologies,and practical implementations across these two critical domains.The review first analyzes the key technical challenges encountered when integrating ILC into precision manufacturing workflows.Through case studies,it evaluates demonstrated improvements in positioning accuracy,surface finish quality,and production throughput.Furthermore,the study examines ILC’s applications in ITS,with particular focus on vehicular motion control applications including autonomous vehicle trajectory tracking,platoon coordination,and traffic signal timing optimization,where its data-driven characteristics enhance adaptability to dynamic environments.Finally,the paper proposes targeted future research directions that are essential for fully realizing ILC’s potential in advancing these interconnected yet distinct fields.
文摘The iterative continuation task(ICT)requires English as a foreign language(EFL)learners to read a segment and write a continuation that aligns with the preceding segment of an English novel with successive turns,offering exposure to diverse grammatical structures and opportunities for contextualized usage.Given the importance of integrating technology into second language(L2)writing and the critical role that grammar plays in L2 writing development,automated written corrective feedback provided by Grammarly has gained significant attention.This study investigates the impact of Grammarly on grammar learning strategies,grammar grit,and grammar competence among EFL college students engaged in ICT.This study employed a mixed-methods sequential exploratory design;56 participants were divided into an experimental group(n=28),receiving Grammarly feedback for ICT,and a control group(n=28),completing ICT without Grammarly feedback.Quantitative results revealed that both groups showed improvements in L2 grammar learning strategies,grit and competence.For the experimental group,significant differences were observed across all variables of L2 grammar learning strategies,grit,and competence between pre-and post-tests.For the control group,significant differences were only observed in the affective dimension of grammar learning strategies,Consistency of Interest(COI)of grammar grit,and grammar competence.However,the control group presented a significantly higher improvement in grammar competence.Qualitative analysis showed both positive and negative perceptions of Grammarly.The pedagogical implications of integrating Grammarly and ICT for L2 grammar development are discussed.
基金supported by the National Key Research and Development Program of China(2023YFF0906502)the Postgraduate Research and Innovation Project of Hunan Province under Grant(CX20240473).
文摘Due to the digital transformation tendency among cultural institutions and the substantial influence of the social media platform,the demands of visual communication keep increasing for promoting traditional cultural artifacts online.As an effective medium,posters serve to attract public attention and facilitate broader engagement with cultural artifacts.However,existing poster generation methods mainly rely on fixed templates and manual design,which limits their scalability and adaptability to the diverse visual and semantic features of the artifacts.Therefore,we propose CAPGen,an automated aesthetic Cultural Artifacts Poster Generation framework built on a Multimodal Large Language Model(MLLM)with integrated iterative optimization.During our research,we collaborated with designers to define principles of graphic design for cultural artifact posters,to guide the MLLM in generating layout parameters.Later,we generated these parameters into posters.Finally,we refined the posters using an MLLM integrated with a multi-round iterative optimization mechanism.Qualitative results show that CAPGen consistently outperforms baseline methods in both visual quality and aesthetic performance.Furthermore,ablation studies indicate that the prompt,iterative optimization mechanism,and design principles significantly enhance the effectiveness of poster generation.
基金Project supported by the National Natural Science Foundation of China (No.10472061)
文摘An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved.
文摘In this paper, Aitken’s extrapolation normally applied to convergent fixed point iteration is extended to extrapolate the solution of a divergent iteration. In addition, higher order Aitken extrapolation is introduced that enables successive decomposition of high Eigen values of the iteration matrix to enable convergence. While extrapolation of a convergent fixed point iteration using a geometric series sum is a known form of Aitken acceleration, it is shown that in this paper, the same formula can be used to estimate the solution of sets of linear equations from diverging Gauss-Seidel iterations. In both convergent and divergent iterations, the ratios of differences among the consecutive values of iteration eventually form a convergent (divergent) series with a factor equal to the largest Eigen value of the iteration matrix. Higher order Aitken extrapolation is shown to eliminate the influence of dominant Eigen values of the iteration matrix in successive order until the iteration is determined by the lowest possible Eigen values. For the convergent part of the Gauss-Seidel iteration, further acceleration is made possible by coupling of the extrapolation technique with the successive over relaxation (SOR) method. Application examples from both convergent and divergent iterations have been provided. Coupling of the extrapolation with the SOR technique is also illustrated for a steady state two dimensional heat flow problem which was solved using MATLAB programming.
文摘In this paper, equivalence between the Mann and Ishikawa iterations for a generalized contraction mapping in cone subset of a real Banach space is discussed.
基金Supported by Shanghai Municipal Foundation of Selected Academic Research and the National Natural Science Foundation of China（10571059,10571060）.
文摘Under the weak Lipschitz condition about the solution of the equation, convergence theorems for a family of iterations with one parameter are obtained. An estimation of the radius of the attraction ball is shown. At last two examples are given.
基金supported by the National Natural Science Foundation of China(40974018)Nationa l863 Plan Projects(2009AA12Z307)
文摘The simultaneous iterations rithms of the ART family. It is used reconstruction technique （SIRT） widely in tomography because of is one of several reconstruction algoits convenience in dealing with large sparse matrices. Its theoretical background and iteration model are discussed at the beginning of this paper. Then, the implementation of the SIRT to reconstruct the three-dimensional distribution of water vapor by simulation is discussed. The results show that the SIRT can function effectively in water vapor tomography, obtain rapid convergence, and be implemented more easily than inversion.
基金Project supported by the National Natural Science Foundation of China(Nos.11971410 and12071404)the Natural Science Foundation of Hunan Province of China(No.2019JJ40279)+2 种基金the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education(Nos.18B064 and 20B564)the China Postdoctoral Science Foundation(Nos.2018T110073 and 2018M631402)the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science(No.2018WK4006)。
文摘Based on local algorithms,some parallel finite element(FE)iterative methods for stationary incompressible magnetohydrodynamics(MHD)are presented.These approaches are on account of two-grid skill include two major phases:find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution,and then locally solve linearized residual subproblems by one of three iterations(Stokes-type,Newton,and Oseen-type)on subdomains with fine grid in parallel to approximate the high frequency component.Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given.Some numerical examples are implemented to verify the algorithm.
文摘This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank<em>-k</em> approximation of a real <em>m</em>×<em>n</em> matrix, <em>A</em>. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, <em>G</em>, this method computes<em> k</em> dominant eigenvectors of <em>G</em>. To see the relation between these methods we assume that <em>G </em>=<em> A</em><sup>T</sup> <em>A</em>. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.
基金supported by the National Natural Science Foundation of China(No.11271298)
文摘This paper considers Stokes and Newton iterations to solve stationary Navier- Stokes equations based on the finite element discretization. We obtain new sufficient conditions of stability and convergence for the two iterations. Specifically, when 0 〈 σ =N｜｜f｜｜-1/v2≤1/√2＋1 , the Stokes iteration is stable and convergent, where N is defined in the paper. When 0 〈 σ ≤5/11, the Newton iteration is stable and convergent. This work gives a more accurate admissible range of data for stability and convergence of the two schemes, which improves the previous results. A numerical test is given to verify the theory.
文摘A new restoration algorithm based on double loops and alternant iterations is proposed to restore the object image effectively from a few frames of turbulence-degraded images, Based on the double loops, the iterative relations for estimating the turbulent point spread function PSF and object image alternately are derived. The restoration experiments have been made on computers, showing that the proposed algorithm can obtain the optimal estimations of the object and the point spread function, with the feasibility and practicality of the proposed algorithm being convincing.
文摘In this paper, we present and analyze modified families of predictor-corrector iterative methods for finding simple zeros of univariate nonlinear equations, permitting near the root. The main advantage of our methods is that they perform better and moreover, have the same efficiency indices as that of existing multipoint iterative methods. Furthermore, the convergence analysis of the new methods is discussed and several examples are given to illustrate their efficiency.
基金This study was supported by the“High level research and training project for professional leaders of teachers in Higher Vocational Colleges in Jiangsu Province”.
文摘In order to improve the performance of time difference of arrival(TDOA)localization,a nonlinear least squares algorithm is proposed in this paper.Firstly,based on the criterion of the minimized sum of square error of time difference of arrival,the location estimation is expressed as an optimal problem of a non-linear programming.Then,an initial point is obtained using the semi-definite programming.And finally,the location is extracted from the local optimal solution acquired by Newton iterations.Simulation results show that when the number of anchor nodes is large,the performance of the proposed algorithm will be significantly better than that of semi-definite programming approach with the increase of measurement noise.
文摘We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.
基金Supported by the Nature Science Foundation of Guangdong Province (020163).
文摘Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.
文摘In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.
