Methodological review demonstrates guaranteed convergence of the QR algorithm in symmetric matrices, highlighting its foundational role in eigenvalue computation.
After a brief sketch of the early days of eigenvalue hunting, the author describes the QR (or orthogonal triangular) matrix factorization algorithm and its major virtues. The symmetric case brings with it guaranteed convergence and an elegant implementation. An account of the impressive discovery of the algorithm brings the article to a close.
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Beresford Ν. Parlett (2000) studied this question.
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