Lecture 8

  • Eugene E. Tyrtyshnikov


Given a square matrix A, a decomposition A = QR, where Q is unitary and R is upper triangular, is said to be the QR decomposition of A. In contrast to the LU decomposition, one does not fear a growth of entries in the case of the QR decomposition. (Why?)


Arithmetic Operation Rectangular Matrix Hessenberg Matrix Reflection Matrix Hessenberg Form 
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  1. 1.
    W. Hoffmann. Iterative algorithms for Gram-Schmidt orthogonalization. Computing 41: 335–348 (1989).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    A. Bjorck and C. C. Paige. Loss and recapture of orthogonality in the modified Gram-Schmidt algorithm. SIAM J. Matrix Anal. Appl. 13(1): 176–190 (1992).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Eugene E. Tyrtyshnikov
    • 1
  1. 1.Institute of Numerical MathematicsRussian Academy of SciencesMoscowRussia

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