Timeline for Shifted QR algorithm—why does the shift help?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2022 at 18:41 | history | edited | LSpice | CC BY-SA 4.0 |
Link while this is on the front page
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| May 18, 2011 at 10:50 | comment | added | Denis Serre | The QR algorithm does not treat efficiently eigenvalues that have the same modulus. Example 1: if $A$ is unitary (then all ev have modulus $1$), the iterates coincide with $A$. Example 2: if $A$ has real entries, the iterates remain real and cannot converge to a triangular form if there is at least one pair of complex conjugate ev. Both cases can be cured with a shift! I do not know what really happens when one ev has multiplicity, but this case cannot be avoided just by a shift. | |
| May 17, 2011 at 16:02 | comment | added | vanvu | Thanks. I see it a bit clearer now. Btw, what happens if there are multiple eigenvalues ? | |
| May 17, 2011 at 8:40 | history | answered | Denis Serre | CC BY-SA 3.0 |