Timeline for bounding roots of a polynomial with Rouche's Theorem
Current License: CC BY-SA 2.5
11 events
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| Feb 25, 2010 at 23:39 | comment | added | Emerton | There is a saying about Zagier (although I don't know if it originates with him) that one day of his time is a week of anybody else's time. | |
| Feb 25, 2010 at 22:11 | comment | added | Mariano Suárez-Álvarez | Out of curiosity: what is the original phrase of Zagier you are paraphrasing? | |
| Feb 25, 2010 at 22:02 | history | edited | user631 | CC BY-SA 2.5 |
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| Feb 25, 2010 at 19:11 | history | edited | user631 | CC BY-SA 2.5 |
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| S Feb 25, 2010 at 11:37 | comment | added | user4230 | ...z=p+iq is a root and p,q are real. However it seems more natural to consider |z|. I hope this makes more sense. | |
| S Feb 25, 2010 at 11:37 | comment | added | user4230 | I would like a bound in terms of k and/or n. One which would work whether or not k is close to 1/n. My method was different in the sense that I took partial derivatives which would tell you the effect of fixing different values for the complex part. Are you simply using the fact that the root would occur roughly twice as far as the turning point? I would like a better lower bound of |1-z_k| where |z_k| is the largest root with positive real part (better than (1-kn)/(1+n) I mean). I actually simply want to find an upper bound on the real part of any root. i.e find an upper bound for p where... | |
| Feb 25, 2010 at 2:19 | history | edited | user631 | CC BY-SA 2.5 |
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| Feb 24, 2010 at 23:01 | comment | added | user4230 | I got the same bound via a different method. I looked at fixing the complex part of z and taking the partial derivative of g(z) with respect to the real part. The first turning point to the left of the root at z=1 is at 1-(1-kn)/((1+n) = (1+k)/(1+n^(-1)). The fact that this is where the turning point lies motivates the fact that there is still some more room to push to the left of this value where a root cannot lie. | |
| Feb 24, 2010 at 22:04 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
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| Feb 24, 2010 at 21:57 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
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| Feb 24, 2010 at 21:34 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |