Roots of bivariate polynomial systems via determinantal representations

B. Plestenjak, M.E. Hochstenbach

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9 Citations (Scopus)
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We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a twoparameter eigenvalue problem. The first determinantal representation is suitable for polynomials with scalar or matrix coecients and consists of matrices with asymptotic order n2=4, where n is the degree of the polynomial. The second representation is useful for scalar polynomials and has asymptotic order n2=6. The resulting method to compute the roots of a system of two bivariate polynomials is very competitive with some existing methods for polynomials up to degree 10, as well as for polynomials with a small number of terms.

Original languageEnglish
Pages (from-to)A765-A788
Number of pages24
JournalSIAM Journal on Scientific Computing
Issue number2
Publication statusPublished - 2016


  • Determinantal representation
  • Polynomial two-parameter eigenvalue problem
  • System of bivariate polynomial equations
  • Twoparameter eigenvalue problem


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