## Abstract

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 language | English |
---|---|

Pages (from-to) | A765-A788 |

Number of pages | 24 |

Journal | SIAM Journal on Scientific Computing |

Volume | 38 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 |

## Keywords

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