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1 results

  • 8 - Eigenvalue Problems

  • from Part I - Numerical Linear Algebra
  • Abner J. Salgado, University of Tennessee, Knoxville, Steven M. Wise, University of Tennessee, Knoxville
  • Book:
    Classical Numerical Analysis
    Published online:
    29 September 2022
    Print publication:
    20 October 2022, pp 197-228

  • Summary

    We present several methods for approximating the spectrum of a matrix. We start by providing coarse estimates using so-called Gershgoring disks. The stability, via the Bauer-Fike theorem is then analyzed. For Hermitian matrices we then present and analyze the power iteration method and its variants. The reduction to Hessenberg form, and the QR algorithm are then presented and analyzed. The chapter then concludes with a discussion of the Golub-Kahan algorithm to compute the SVD.