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A Preconditioned Conjugate Gradient Algorithm for Solving Equation Systems with Non-positive Definite Sparse Matrices

机译：求解带正定稀疏矩阵方程组的预处理共轭梯度算法

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A new preconditioned conjugate gradient algorithm is presented to solve the system of equations with non-positive definite sparse coefficient matrixes. The algorithm is based on the conjugate gradient method, but employing the incomplete LU factorization approach as the pre-conditioner. By introducing this pre-conditioner the convergence rate of the iterative solution process is increased considerably. The solution results indicate this new preconditioned conjugate gradient algorithm is suitable for solving the equation systems with symmetric non-positive definite sparse matrixes, which appear in the finite element system with anisotropic media.

机译：提出了一种新的预处理共轭梯度算法来求解带有非正定稀疏系数矩阵的方程组。该算法基于共轭梯度法，但采用不完全LU分解方法作为预处理器。通过引入此预处理器，可大大提高迭代求解过程的收敛速度。求解结果表明，该新的预处理共轭梯度算法适用于求解对称各向异性非正定稀疏矩阵的方程组，该方程组出现在具有各向异性介质的有限元系统中。

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来源
《Applied electromagnetics(III)》|2001年|p.203-206|共4页
会议地点 Hangzhou(CN);Hangzhou(CN)
作者
Qin Chen; Zhanghong Tang; Jiansheng Yuan;
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作者单位

Department of Electrical Engineering, Tsinghua University, Beijing, China;

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原文格式 PDF
正文语种 eng
中图分类物理学;
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2. LOW-RANK FACTORIZATIONS IN DATA SPARSE HIERARCHICAL ALGORITHMS FOR PRECONDITIONING SYMMETRIC POSITIVE DEFINITE MATRICES [J] . Agullo Emmanuel, Darve Eric, Giraud Luc, SIAM Journal on Matrix Analysis and Applications . 2018,第4期

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3. Gradient-based iterative algorithm for solving the generalized coupled Sylvester-transpose and conjugate matrix equations over reflexive (anti-reflexive) matrices [J] . Fatemeh Panjeh Ali Beik, Davod Khojasteh Salkuyeh, Mahmoud Mohseni Moghadam Transactions of the Institute of Measurement and Control . 2014,第1期

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4. A Preconditioned Conjugate Gradient Algorithm for Solving Equation Systems with Non-positive Definite Sparse Matrices [C] . Qin Chen, Zhanghong Tang, Jiansheng Yuan, Asian symposium on applied electromagnetics . 2001

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5. Preconditioning sparse matrices for computing eigenvalues and solving linear systems of equations. [D] . Chen, Tzu-Yi. 2001

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6. Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications [O] . Yongchun Xu, Jinyu Guan, Yanxia Tang, -1

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7. A Parallel Preconditioned Conjugate Gradient Package for Solving Sparse Linear Systems on a Cray Y-MP [O] . Michael A. Heroux, Phuong Vu, Chao Yang 1991

机译：并行预处理共轭梯度包，用于求解Cray Y-MP上的稀疏线性系统
8. Preconditioned Conjugate Gradient Algorithms and Software for Solving Large Sparse Linear Systems [R] . Young, D. M. , Jea, K. C. , Mai, T. Z. 1987

机译：预处理共轭梯度算法及求解大型稀疏线性系统的软件

A Preconditioned Conjugate Gradient Algorithm for Solving Equation Systems with Non-positive Definite Sparse Matrices

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