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Workshop

Student presentation: Algorithms for counting real roots

  • Clemens Brüser (TU Dresden, Dresden, Germany)
G3 10 (Lecture hall)

Abstract

In the 17th century, Rene Descarte first developed ideas to count the number of positive real roots of a univariate real polynomial based on its coefficients alone. These ideas have come a long way and today provide us with useful algorithms to answer the following questions:

- Given f in R[x], how many of its roots are real? How many are positive? How many lie in [0,1]?

- Given f,g in R[x], how many points a are there such that both f(a) = 0 and g(a) > 0?

We will discuss some of these algorithms and how they can be applied to answer some of these questions.

Links

Mirke Olschewski

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Chiara Meroni

Max Planck Institute for Mathematics in the Sciences