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Explicit determinantal representations of up to quintic bivariate polynomials. (English) Zbl 1401.65035
Summary: For bivariate polynomials of degree $$n\leq 5$$ we give fast numerical constructions of determinantal representations with $$n\times n$$ matrices. Unlike some other existing constructions, our approach returns matrices of the smallest possible size $$n\times n$$ for all (not just generic) polynomials of degree $$n$$ and does not require any symbolic computation. We can apply these linearizations to numerically compute the roots of a system of two bivariate polynomials by using numerical methods for the two-parameter eigenvalue problems.

##### MSC:
 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65H04 Numerical computation of roots of polynomial equations 65F50 Computational methods for sparse matrices 13P15 Solving polynomial systems; resultants 14M12 Determinantal varieties 14Q05 Computational aspects of algebraic curves
##### Keywords:
bivariate polynomial; determinantal representation
BiRoots; Matlab
Full Text:
##### References:
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