成果/Result
- A projection method based on extended Krylov subspaces for solving Sylvester equations被引量：44收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构： Department of Mathematics and Computational Science; Department of Mathematics; School of Mathematical Sciences; Key Laboratory of Mathematics for Nonlinear Sciences
- 来源：World Academy of Science, Engineering and Technology 2011
- 关键词：Numerical methods - Inverse problems - Matrix algebra
- Krylov subspace type methods for solving projected generalized continuous-time Lyapunov equations被引量：42收藏
- 作者：Zhou, Yujian Lin, Yiqin Bao, Liang
- 机构： Hunan University of Science and Engineering; East China University of Science and Technology
- 来源：WSEAS Transactions on Mathematics 2012
- 关键词：Lyapunov functions - Continuous time systems
- Restarted generalized second-order krylov subspace methods for solving quadratic eigenvalue problems被引量：40收藏
- 作者：Zhou, Liping Bao, Liang Lin, Yiqin Wei, Yimin Wu, Qinghua
- 机构： Department of Mathematics and Computational Science; Department of Mathematics; School of Mathematical Sciences; Key Laboratory of Mathematics for Nonlinear Sciences
- 来源：International Journal of Computational and Mathematical Sciences 2010
- 关键词：Degrees of freedom (mechanics) - Eigenvalues and eigenfunctions - Numerical methods - Vectors - Problem solving - Acoustic fields - Fluid mechanics
- A schur method for solving projected continuous-time sylvester equations被引量：33收藏
- 作者：Lin, Yiqin Bao, Liang Wu, Qinghua Zhou, Liping
- 机构： Department of Mathematics and Computational Science; Department of Mathematics; Department of Mathematics and Computational Science; Department of Mathematics and Computational Science
- 来源：International Journal of Computational and Mathematical Sciences 2010
- 关键词：Numerical methods - Continuous time systems
- Model-order reduction of large-scale kth-order linear dynamical systems via a kth-order Arnoldi method被引量：30收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构： Department of Mathematics and Computational Science; Department of Mathematics; Institute of Mathematics
- 来源：International Journal of Computer Mathematics 2010
- 关键词：Dynamical systems - Linear control systems - Numerical methods - Eigenvalues and eigenfunctions
- Order reduction of bilinear MIMO dynamical systems using new block Krylov subspaces被引量：27收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构：Hunan Univ Sci & Engn;E China Univ Sci & Technol;Fudan Univ;Fudan Univ
- 来源：COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009
- 关键词：Bilinear system Order-reduced modeling Moment matching Block Krylov subspace Projection method
- A direct method for solving projected generalized continuous-time Sylvester equations被引量：23收藏
- 作者：Lin, Yiqin Bao, Liang Cao, Yanhua Zhou, Liping
- 机构： Department of Mathematics and Computational Science; Department of Mathematics; Department of Mathematics
- 来源：Journal of Control Theory and Applications 2012
- 关键词：Continuous time systems - Numerical methods
- Convergence analysis of a variant of the Newton method for solving nonlinear equations被引量：21收藏
- 作者：Lin, Yiqin Bao, Liang Jia, Xianzheng
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn;Shandong Univ Technol
- 来源：COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010
- 关键词：Nonlinear system Newton method Modified Newton method Convergence behavior Nonsymmetric algebraic Riccati equation M-matrix
- A new generalized successive-overrelaxation iteration method for solving saddle point problems被引量：20收藏
- 作者：Siting, Wu Liang, Bao Jingxuan, Huang
- 机构： School of Science
- 来源：ACM International Conference Proceeding Series 2021
- 关键词：Matrix algebra - Numerical methods
- On the generalized structure-preserving doubling algorithm for Generalized Discrete-time Algebraic Riccati equations被引量：18收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构： Institute of Computational Mathematics; Department of Mathematics; Institute of Mathematics; Key Laboratory of Mathematics for Nonlinear Sciences
- 来源：Journal of Information and Computational Science 2011
- 关键词：Hamiltonians - Mathematical transformations - Algebra - Riccati equations
- Model-order reduction of large-scale kth-order linear dynamical systems via a kth-order Arnoldi method被引量：18收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构：Fudan Univ;Fudan Univ;Hunan Univ Sci & Engn;E China Univ Sci & Technol
- 来源：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2010
- 关键词：high-order linear system kth-order Krylov subspace kth-order Arnoldi procedure model-order reduction polynomial eigenvalue problem
- A modified Newton method for solving non-symmetric algebraic Riccati equations arising in transport theory被引量：17收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构：Fudan Univ;Fudan Univ;Hunan Univ Sci & Engn;E China Univ Sci & Technol
- 来源：IMA JOURNAL OF NUMERICAL ANALYSIS 2008
- 关键词：non-symmetric algebraic Riccati equation transport theory minimal positive solution M-matrix modified Newton method
- Inexact iterative methods for solving matrix Riccati equations arising in stochastic control被引量：17收藏
- 作者：Lin, Yiqin Bao, Liang
- 机构： Institute of Computational Mathematics; Department of Mathematics
- 来源：Journal of Information and Computational Science 2010
- 关键词：Numerical methods - Stochastic systems - Newton-Raphson method - Stochastic control systems
- Convergence analysis of the Newton-Shamanskii method for a nonsymmetric algebraic Riccati equation被引量：14收藏
- 作者：Lin, Yiqin Bao, Liang
- 机构：Hunan Univ Sci & Engn;E China Univ Sci & Technol
- 来源：NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2008
- 关键词：nonsymmetric algebraic Riccati equation transport theory minimal positive solution M-matrix Newton-Shamanskii method
- Simpler GMRES with deflated restarting被引量：10收藏
- 作者：Lin, Yiqin Bao, Liang Wu, Qinghua
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn
- 来源：MATHEMATICS AND COMPUTERS IN SIMULATION 2012
- 关键词：Linear system Eigenvector Harmonic Ritz vector GMRES Simpler GMRES Restarting
- Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation被引量：9收藏
- 作者：Tang, Yaoping Bao, Liang Lin, Yiqin
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn
- 来源：INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2011
- 关键词：perturbation analysis condition number linear asymptotic bound generalized Sylvester equation generalized Lyapunov equation
- Matrix Sign Function Methods for Solving Projected Generalized Continuous-Time Sylvester Equations被引量：8收藏
- 作者：Lin, Yiqin Bao, Liang Wei, Yimin
- 机构：Hunan Univ Sci & Engn;E China Univ Sci & Technol;Fudan Univ
- 来源：IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2010
- 关键词：C-stable matrix pencil matrix sign function projected generalized Sylvester equation
- Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems被引量：6收藏
- 作者：Bao, Liang Lin, Yiqin Wei, Yimin
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn;Fudan Univ;Fudan Univ
- 来源：NUMERICAL ALGORITHMS 2009
- 关键词：Polynomial eigenvalue problem Generalized Krylov subspace Generalized Arnoldi procedure Projection technique Refined technique Restarting
- On the convergence rate of an iterative method for solving nonsymmetric algebraic Riccati equations被引量：4收藏
- 作者：Lin, Yiqin Bao, Liang Wu, Qinghua
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn
- 来源：COMPUTERS & MATHEMATICS WITH APPLICATIONS 2011
- 关键词：Nonsymmetric algebraic Riccati equation Transport theory Minimal positive solution Iterative method Convergence rate
- 求解非埃尔米特正定方程组的广义LHSS迭代法被引量：3收藏
- 作者：初鲁 鲍亮 董贝贝
- 机构：华东理工大学理学院
- 来源：《浙江大学学报（理学版）》 2018
- 关键词：非埃尔米特正定方程组 LHSS迭代法 谱半径
- 摘要：基于矩阵的埃尔米特和反埃尔米特分解,李良等给出了一类求解非埃尔米特正定方程组的LHSS迭代法,在系数矩阵的埃尔米特和非埃尔米特之间进行了非对称迭代,在较松弛的约束条件下即可获得收敛结果.本文对该方法做进一步研究,给出了一...
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- 求解正定线性方程组的外推的PSS迭代方法被引量：2收藏
- 作者：吴思婷 鲍亮 黄景宣
- 机构：华东理工大学数学学院
- 来源：《华东理工大学学报（自然科学版）》 2022
- 关键词：正定线性方程组 PSS迭代方法 EHSS迭代方法 谱半径 收敛性
- 摘要：为了更高效地求解大型稀疏正定线性方程组,提出了一种外推的正定和反Hermitian迭代方法。新方法首先对系数矩阵进行正定和反Hermitian分裂(PSS),再构造出了一种新的非对称二步迭代格式,同时理论分析了新方法的收...
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- Augmented Arnoldi-Tikhonov Regularization Methods for Solving Large-Scale Linear Ill-Posed Systems被引量：1收藏
- 作者：Lin, Yiqin Bao, Liang Cao, Yanhua
- 机构：Hunan Univ Sci & Engn;E China Univ Sci & Technol;North China Elect Power Univ
- 来源：MATHEMATICAL PROBLEMS IN ENGINEERING 2013
- 关键词：Problem solving
- 浅谈考研题中特征值和特征向量的计算被引量：1收藏
- 作者：鲍亮 林辉球 王圣强
- 机构：华东理工大学数学学院
- 来源：《高等数学研究》 2025
- 关键词：特征值 特征向量
- 摘要：本文首先回顾了矩阵特征值的相关概念和性质,给出了一类特殊矩阵特征值和特征向量的简便计算方法,并结合全国硕士研究生入学统一考试的数学试题实例进行了讨论.最后讨论了特征值和特征向量的一个具体应用.
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- 预条件Krylov子空间法求解耦合Sylvester矩阵方程被引量：1收藏
- 作者：徐冬梅 鲍亮 蔡兆克
- 机构：华东理工大学数学系
- 来源：《华东理工大学学报（自然科学版）》 2015
- 关键词：预条件 Krylov子空间 耦合Sylvester矩阵方程
- 摘要：基于Krylov子空间方法,求解耦合Sylvester矩阵方程并给出了预条件全局正交化方法以及预条件全局极小残量法两种方法,同时给出这两种方法的一些理论结果。数值实验的结果表明,采用预条件Krylov子空间方法求解该类方...
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- 预条件的平方Smith法求解大型Sylvester矩阵方程被引量：1收藏
- 作者：蔡兆克 鲍亮 徐冬梅
- 机构：华东理工大学理学院
- 来源：《计算机工程与科学》 2017
- 关键词：平方Smith算法 Sylvester方程 ADI 预条件算子 Krylov子空间
- 摘要：提出了一种预条件的平方Smith算法求解大型连续Sylvester矩阵方程,该算法利用交替方向隐式迭代(ADI)来构造预条件算子,将原方程转换为非对称Stein方程,并在Krylov子空间中应用平方Smith法迭代产生低...
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- On the Perturbation Bounds of Projected Generalized Continuous-Time Sylvester Equations被引量：1收藏
- 作者：Zhou, Yujian Bao, Liang Lin, Yiqin
- 机构：E China Univ Sci & Technol;Hunan Univ Sci & Engn
- 来源：MATHEMATICAL PROBLEMS IN ENGINEERING 2012
- On the loss of orthogonality in the second-order Arnoldi process被引量：1收藏
- 作者：Lin, Yiqin Bao, Liang
- 机构：Hunan Univ Sci & Engn;East China Univ Sci & Technol
- 来源：JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2011
- 关键词：Second-order Krylov subspace Second-order Arnoldi process Rounding error analysis Modified Gram-Schmidt algorithm Orthogonalization
- 预条件平方Smith法求解连续Lyapunov方程被引量：1收藏
- 作者：蔡兆克 鲍亮 初鲁
- 机构：华东理工大学数学系
- 来源：《华东理工大学学报（自然科学版）》 2016
- 关键词：连续Lyapunov方程 预条件 平方Smith算法 ADI Krylov空间
- 摘要：探讨了如何数值求解连续时间的Lyapunov矩阵方程AX+XA^T+BB^T=0,给出了一种预条件的平方Smith算法,该算法首先利用交替方向隐式法即ADI法处理连续Lyapunov方程,构造出含ADI参数的对称Stei...
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- Residual-Based Simpler Block GMRES for Nonsymmetric Linear Systems with Multiple Right-Hand Sides被引量：1收藏
- 作者：Wu, Qinghua Bao, Liang Lin, Yiqin
- 机构：Xiangtan Univ;Hunan Univ Sci & Engn;East China Univ Sci & Technol
- 来源：ADVANCES IN MATHEMATICAL PHYSICS 2018
- 非Hermitian正定线性方程组的外推的广义HSS方法被引量：1收藏
- 作者：吴思婷 鲍亮
- 机构：华东理工大学数学学院
- 来源：《计算机工程与科学》 2022
- 关键词：非Hermitian正定线性方程组 GHSS迭代方法 EHSS迭代方法 收敛性
- 摘要：探讨了如何高效求解非Hermitian正定线性方程组,提出了一种外推的广义Hermitian和反Hermitian (EGHSS)迭代方法。首先,根据矩阵的广义Hermitian和反Hermitian分裂,构造出了一种新...
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