Linear Algebraic Solvers and Eigenvalue Analysis

Henk A. van der Vorst, Kees Vuik

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


This chapter gives an overview of the most widely used numerical methods for the solution of linear systems of equations and for eigenproblems, including direct methods and iterative methods. Iterative methods are often used in combination with the so-called preconditioning operators. We will give a brief overview of the various preconditioners that exist. For eigenproblems of the type inline image, the QR method is discussed. The QR method is expensive for larger values of inline image, and for these larger values, a number of iterative methods, including the Lanczos method, Arnoldi's method, and the Jacobi–Davidson method are shown.
Original languageEnglish
Title of host publicationEncyclopedia of Computational Mechanics
EditorsE. Stein, R. de Borst, T.J.R. Hughes
Place of PublicationChichester
PublisherJohn Wiley & Sons
Number of pages28
EditionSecond Edition
ISBN (Electronic)9781119176817
Publication statusPublished - 2017


  • Linear systems
  • direct methods
  • iterative methods
  • Krylov solvers
  • preconditioning
  • eigensolvers
  • QR method
  • Lanczos
  • Arnoldi
  • Jacobi–Davidson


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