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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:283

Article

Bai, Zhong-Zhi^1,2 

[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;   

DOI  :  10.1016/j.cam.2015.01.025

来源: Elsevier

【 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.

【 授权许可】

Free