QR algorithm with explicit shifts
hi,
i am using the QR algorithm with explicit shifts to find the eigenvalues of
a real or complex matrix.
the way i have it set up at present is that it selects a shift (a wilkinson
shift taken from the eigenvalues of the bottom right hand corner 2 x 2
submatrix) , and then carries out iterations of the QR algorithm until one
of the eigenvalues converges. it then stops, deflates the matrix, selects
another shift and carries on with the QR algorithm until the next eigenvalue
converges.
my question is, would it be possible to select a new shift after every
iteration , rather than waiting for convergence? if so would there be any
advantage in doing this, with regards to how quickly overall convergence is
acheived etc?
thanks
.
Relevant Pages
- Re: incorrect convergence of qr algorithm
... >> i have written an eigenvalue finder that uses the qr algorithm, ... i seem to get the wrong values upon convergence. ... have all eigenvalues on the unit circle in the complex plane. ... then complex eigenvalues appear as complex conjugates and no real shift can break ...
(sci.math.num-analysis) - Re: convergence of QR-algorithm
... Bill, yes I'm doing all of that., alongside using a shift that is the ... calculate the eigenvalues of this. ... In either case the bottom two elements below the diagonal should ... the one I'm using as it involves more calculation at each iteration. ...
(sci.math.num-analysis) - Re: QR algorithm with explicit shifts
... and then carries out iterations of the QR algorithm until one ... >of the eigenvalues converges. ... >another shift and carries on with the QR algorithm until the next eigenvalue ... with regards to how quickly overall convergence is ...
(sci.math.num-analysis) - Re: QR algorithm
... >I have written a computer routine that uses the QR algorithm to find the ... >eigenvalues of a real or complex matrix, and it works fine, always producing ... if the diagonal elements of the matrix are the same then the ... >the diagonal elements being all the same, and then to shift the produced ...
(sci.math.num-analysis) - Re: Why the error in this 2x2 eigenvalue computation?
... (Peter Spellucci) ... double shift is a shift and its conjugate, but I thought it would be ... I don't believe that eig() will do shifts on a 2 by 2 problem, ... those shifts are taken anyway as the eigenvalues of the right lower ...
(sci.math.num-analysis) |
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