Campus Event Calendar

Event Entry

What and Who

On Descartes' rule

Arno Eigenwillig
Max-Planck-Institut für Informatik - D1
AG1 Mittagsseminar (others' work)
AG 1, AG 3, AG 5, RG2, AG 2, AG 4, RG1, SWS  
AG Audience

Date, Time and Location

Friday, 23 February 2007
45 Minutes
E1 4


Descartes' rule of signs gives an upper bound for the number of positive real roots of a univariate real polynomial. (This has close links to the variation-diminishing property of Bézier curves.) Descartes' rule is a popular tool in algorithms for real root isolation. Their analysis requires theorems of the form: Descartes' rule counts at most so-and-so many roots, provided that some condition holds.

As a result of literature research, I will present a few such theorems and proofs from the early 20th century. Some of this historic material tends to be overlooked in contemporary research literature on algorithms for real root isolation.

While the results and proofs I present should be _understandable_ to anyone with basic math education, they are probably most _interesting_ for listeners with a background in Computer Algebra or Exact Non-linear Geometry.


Arno Eigenwillig
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Tags, Category, Keywords and additional notes

Notice the unusual time. I have followed a request to avoid a collision with the AVACS seminar.

Arno Eigenwillig, 02/14/2007 14:22
Arno Eigenwillig, 02/14/2007 14:21 -- Created document.