Convergence of the Francis shifted QR algorithm on normal matrices
نویسندگان
چکیده
منابع مشابه
Convergence of the shifted QR algorithm for unitary Hessenberg matrices
This paper shows that for unitary Hessenberg matrices the QR algorithm, with (an exceptional initial-value modification of) the Wilkinson shift, gives global convergence; moreover, the asymptotic rate of convergence is at least cubic, higher than that which can be shown to be quadratic only for Hermitian tridiagonal matrices, under no further assumption. A general mixed shift strategy with glob...
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Global and asymptotic convergence properties for the QR algorithm with Francis double shift are established for certain orthogonal similarity classes of 4 x 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.
متن کاملGlobal Convergence of the Basic QR Algorithm on Hessenberg Matrices*
0. Introduction. The QR algorithm was developed by Francis (1960) to find the eigenvalues (or roots) of real or complex matrices. We shall consider it here in the context of exact arithmetic. Sufficient conditions for convergence, listed in order of increasing generality have been given by Francis [1], Kublanovskaja [3], Parlett [4], and Wilkinson [8]. It seems that necessary and sufficient con...
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0. Introduction. The QR algorithm was developed by Francis (1960) to find the eigenvalues (or roots) of real or complex matrices. We shall consider it here in the context of exact arithmetic. Sufficient conditions for convergence, listed in order of increasing generality have been given by Francis [1], Kublanovskaja [3], Parlett [4], and Wilkinson [8]. It seems that necessary and sufficient con...
متن کاملA Fast QR Algorithm for Companion Matrices
It has been shown in [4, 5, 6, 31] that the Hessenberg iterates of a companion matrix under the QR iterations have low off-diagonal rank structures. Such invariant rank structures were exploited therein to design fast QR iteration algorithms for finding eigenvalues of companion matrices. These algorithms require only O(n) storage and run in O(n) time where n is the dimension of the matrix. In t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1994
ISSN: 0024-3795
DOI: 10.1016/0024-3795(94)90010-8