Timeline for Why is it so hard to find the roots of polynomial equations?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2021 at 22:14 | comment | added | robjohn♦ | @BrianKennedy: Neil's link seems to be working for me, now. | |
| Jun 20, 2021 at 12:11 | comment | added | Brian Kennedy | Unfortunately, both links are failing now (anyone have a working link?); so, I am not sure if that paper makes the point or not. But the blurb on Wikipedia somewhat alludes to some good intuition. Here's my take: with higher order polynomials, you can closely match almost any shape curve you want. HOWEVER, just very tiny changes in the coefficients can cause dramatic changes in the resulting curve, moving the roots dramatically. Such instability makes solving for those roots problematic... particularly in real-world scenarios where things are uncertain. | |
| May 1, 2015 at 13:42 | comment | added | J. M. ain't a mathematician | @I.J.Kennedy, Neil has given you a working link; thank him. | |
| Apr 6, 2015 at 22:07 | comment | added | Neil | I think I found it. maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/… | |
| Oct 25, 2014 at 23:48 | comment | added | I. J. Kennedy | @Ｊ.Ｍ. This link is broken. | |
| Apr 20, 2011 at 8:51 | comment | added | J. M. ain't a mathematician | Jim Wilkinson's prize-winning article can be read here; briefly, one frequent source of trouble in numerical polynomial root finding is our habit of expressing polynomials in the monomial basis, and it happens that there are polynomials like $\prod_i (x-i)$ that numerically behave very poorly in rootfinding when expressed in the monomial basis. | |
| Apr 20, 2011 at 6:43 | history | answered | Yuval Filmus | CC BY-SA 3.0 |