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 |
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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