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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Linear convergence in the shifted $QR$ algorithm

Authors: Steve Batterson and David Day
Journal: Math. Comp. 59 (1992), 141-151
MSC: Primary 65F15
MathSciNet review: 1134713
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Abstract: Global and asymptotic convergence properties for the QR algorithm with Francis double shift are established for certain orthogonal similarity classes of $4 \times 4$ real matrices. It is shown that in each of the classes every unreduced Hessenberg matrix will decouple and that the rate of decoupling is almost always linear. The effect of the EISPACK exceptional shift strategy is shown to be negligible.

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Article copyright: © Copyright 1992 American Mathematical Society