Sturm's method in counting roots of random polynomial equations

Efraim Shmerling, Kenneth J. Hochberg

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The problem of finding the probability distribution of the number of zeros in some real interval of a random polynomial whose coefficients have a given continuous joint density function is considered. An algorithm which enables one to express this probability as a multiple integral is presented. Formulas for the number of zeros of random quadratic polynomials and random polynomials of higher order, some coefficients of which are non-random and equal to zero, are derived via use of the algorithm. Finally, the applicability of these formulas in numerical calculations is illustrated.

Original languageEnglish
Pages (from-to)203-218
Number of pages16
JournalMethodology and Computing in Applied Probability
Issue number2
StatePublished - 2004


  • Random polynomial
  • Sturm's method


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