Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there a general bound on a polynomial's root with the largest norm?

When Rouche's theorem is used, it still seems that the polynomial's root with the largest norm still needs to be found if we want a tight bound.

share|cite|improve this question

The Eneström-Kakeya theorem is helpful if the coefficients of the polynomial in question are all real and positive. Essentially, the zeros lie within the circle whose radius is the largest ratio of consecutive coefficients of the polynomial. Here is a good reference (PDF).

There are some generalizations, for instance when the coefficients lie in a given sector symmetric about the positive real axis. I could provide further references if this is what you're looking for.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.