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Algorithms for the Nonsymmetric Eigenvalue Problem

In: Numerical Linear Algebra: Theory and Applications

Author

Listed:
  • Larisa Beilina

    (Chalmers University of Technology and University of Gothenburg, Department of Mathematical Sciences)

  • Evgenii Karchevskii

    (Kazan Federal University, Department of Applied Mathematics)

  • Mikhail Karchevskii

    (Kazan Federal University, Department of Computational Mathematics)

Abstract

In thisNonsymmetric eigenvalue problems 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.

Suggested Citation

  • Larisa Beilina & Evgenii Karchevskii & Mikhail Karchevskii, 2017. "Algorithms for the Nonsymmetric Eigenvalue Problem," Springer Books, in: Numerical Linear Algebra: Theory and Applications, chapter 0, pages 345-374, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-57304-5_10
    DOI: 10.1007/978-3-319-57304-5_10
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