Numerische Mathematik

, Volume 40, Issue 1, pp 47–56 | Cite as

Fast Givens rotations for orthogonal similarity transformations

  • Wolfgang Rath


Fast Givens rotations with half as many multiplications are proposed for orthogonal similarity transformations and a matrix notation is introduced to describe them more easily. Applications are proposed and numerical results are examined for the Jacobi method, the reduction to Hessenberg form and the QR-algorithm for Hessenberg matrices. It can be seen that in general fast Givens rotations are competitive with Householder reflexions and offer distinct advantages for sparse matrices.

Subject Classifications

AMS (MOS): 65F30 CR: 5.14 


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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Wolfgang Rath
    • 1
  1. 1.AhlenGermany

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