Algorithms for the Nonsymmetric Eigenvalue Problem

  • Larisa BeilinaEmail author
  • Evgenii Karchevskii
  • Mikhail Karchevskii


In this chapter, we will present the main algorithms for solving the nonsymmetric eigenvalue problem using direct methods. Direct methods are usually applied to dense matrices, and iterative methods such as the Rayleigh–Ritz method and Lanczos’s algorithm are applied to sparse matrices. Iterative methods usually can compute not all of the eigenvalues and eigenvectors, but only some subset, and their convergence depends on the structure of the matrix.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Larisa Beilina
    • 1
    Email author
  • Evgenii Karchevskii
    • 2
  • Mikhail Karchevskii
    • 3
  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGothenburgSweden
  2. 2.Department of Applied MathematicsKazan Federal UniversityKazan, Tatarstan RepublicRussia
  3. 3.Department of Computational MathematicsKazan Federal UniversityKazan, Tatarstan RepublicRussia

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