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

  • Bai Z
  • 9


    Mendeley users who have this article in their library.
  • N/A


    Citations of this article.


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 preconditioners 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.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in


  • Zhong-zhi Bai

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free