Bounds for resultants of univariate and bivariate polynomials

Yuval Bistritz, Alexander Lifshitz

Research output: Contribution to journalArticlepeer-review

Abstract

The paper considers bounds on the size of the resultant for univariate and bivariate polynomials. For univariate polynomials we also extend the traditional representation of the resultant by the zeros of the argument polynomials to formal resultants, defined as the determinants of the Sylvester matrix for a pair of polynomials whose actual degree may be lower than their formal degree due to vanishing leading coefficients. For bivariate polynomials, the resultant is a univariate polynomial resulting by the elimination of one of the variables, and our main result is a bound on the largest coefficient of this univariate polynomial. We bring a simple example that shows that our bound is attainable and that a previous sharper bound is not correct.

Original languageEnglish
Pages (from-to)1995-2005
Number of pages11
JournalLinear Algebra and Its Applications
Volume432
Issue number8
DOIs
StatePublished - 1 Apr 2010

Keywords

  • Bezoutian
  • Hadamard bound
  • Resultant
  • Sylvester matrix

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