The QR and QL Algorithms for Symmetric Matrices

@article{Bowdler1971TheQA,
title={The QR and QL Algorithms for Symmetric Matrices},
author={H. Bowdler and R. Martin and C. Reinsch and J. H. Wilkinson},
journal={Numerische Mathematik},
year={1971},
volume={11},
pages={227-240}
}
The QR algorithm as developed by Francis [2] and Kublanovskaya [4] is conceptually related to the LR algorithm of Rutishauser [7]. It is based on the observation that if $$A = QR{\text{ and }}B{\text{ = }}RQ{\text{,}}$$ (1) where Q is unitary and R is upper-triangular then $$B = RQ = {Q^H}AQ,$$ (2) that is, B is unitarily similar to A. By repeated application of the above result a sequence of matrices which are unitarily similar to a given matrix A 1 may be derived from the… Expand
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