Motivations and realizations of Krylov subspace methods for large sparse linear systems

被引:133
作者
Bai, Zhong-Zhi [1 ,2 ]
机构
[1] Shanghai Univ, Qian Weichang Coll, Shanghai 200436, Peoples R China
[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing 100190, Peoples R China
关键词
Linear system; Direct method; Iterative method; Krylov subspace; Preconditioning; MULTILEVEL PRECONDITIONING METHODS; HERMITIAN SPLITTING METHODS; ITERATIVE METHODS; RELAXATION METHODS; GMRES CONVERGENCE; MATRICES; BOUNDS;
D O I
10.1016/j.cam.2015.01.025
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We briefly introduce typical and important direct and iterative methods for solving systems of linear equations, concretely describe their fundamental characteristics in viewpoints of both theory and applications, and clearly clarify the substantial differences among these methods. In particular, the motivations of searching the solution of a linear system in a Krylov subspace are described and the algorithmic realizations of the generalized minimal residual (GMRES) method are shown, and several classes of state-of-the-art algebraic pre-conditioners are briefly reviewed. All this is useful for correctly, deeply and completely understanding the application scopes, theoretical properties and numerical behaviors of these methods, and is also helpful in designing new methods for solving systems of linear equations. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:71 / 78
页数:8
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