Iterative methods for solving linear systems
Iterative methods for solving linear systems
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DOI：
10.1137/1.9781611970937
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
A. Greenbaum
中科院分区：
文献类型：
--
作者：
A. Greenbaum
算法列表介绍。线性代数相关符号的研究现状综述。第1部分：Krylov子空间近似。一些迭代方法。简单迭代正演(1)和最陡下降正演(2)与CG正演、MINRES和GMRES从Lanczos算法推导MINRES和CG 3。CG、MINRES和GMRES的误差范围。厄米问题- cg和MINRES非厄米问题- gmres有限精度算法的影响。5. Lanczos算法&一种假设MINRES/CG实现&矩阵补全问题正交多项式BiCG及相关方法。双面Lanczos算法双共轭梯度算法拟最小残差算法BiCG与QMR的关系共轭梯度平方算法BiCGSTAB算法我该用哪种方法？6. 近似最优逼近是否存在短递归？费伯和曼特菲尔结果的启示各种各样的问题。对称问题误差估计和停止准则可达到精度多右手边和块方法的计算机实现第二部分。预调节器。8。概述和预条件算法。两个例题。扩散方程和输运方程预调节器的比较。正则分裂与CG算法的比较正则分裂与最优对角和块对角预处理11。不完整的分解。修正的不完全Cholesky分解多重网格和区域分解方法。多网格方法领域分解方法的基本思想。
List of Algorithms Preface 1. Introduction. Brief Overview of the State of the Art Notation Review of Relevant Linear Algebra Part I. Krylov Subspace Approximations. 2. Some Iteration Methods. Simple Iteration Orthomin(1) and Steepest Descent Orthomin(2) and CG Orthodir, MINRES, and GMRES Derivation of MINRES and CG from the Lanczos Algorithm 3. Error Bounds for CG, MINRES, and GMRES. Hermitian Problems-CG and MINRES Non-Hermitian Problems-GMRES 4. Effects of Finite Precision Arithmetic. Some Numerical Examples The Lanczos Algorithm A Hypothetical MINRES/CG Implementation A Matrix Completion Problem Orthogonal Polynomials 5. BiCG and Related Methods. The Two-Sided Lanczos Algorithm The Biconjugate Gradient Algorithm The Quasi-Minimal Residual Algorithm Relation Between BiCG and QMR The Conjugate Gradient Squared Algorithm The BiCGSTAB Algorithm Which Method Should I Use? 6. Is There A Short Recurrence for a Near-Optimal Approximation? The Faber and Manteuffel Result Implications 7. Miscellaneous Issues. Symmetrizing the Problem Error Estimation and Stopping Criteria Attainable Accuracy Multiple Right-Hand Sides and Block Methods Computer Implementation Part II. Preconditioners. 8. Overview and Preconditioned Algorithms. 9. Two Example Problems. The Diffusion Equation The Transport Equation 10. Comparison of Preconditioners. Jacobi, Gauss--Seidel, SOR The Perron--Frobenius Theorem Comparison of Regular Splittings Regular Splittings Used with the CG Algorithm Optimal Diagonal and Block Diagonal Preconditioners 11. Incomplete Decompositions. Incomplete Cholesky Decomposition Modified Incomplete Cholesky Decomposition 12. Multigrid and Domain Decomposition Methods. Multigrid Methods Basic Ideas of Domain Decomposition Methods.