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A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations

Tijdschriftbijdrage - Tijdschriftartikel

We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$ variables. We assume that the polynomials are generic in the sense that the number of solutions in $\mathbb{C}^n$ equals the B\'ezout number. The main contribution of this paper is an automated choice of basis for $\mathbb{C}[x]/I$, which is crucial for the feasibility of normal form methods in finite precision arithmetic. This choice is based on numerical linear algebra techniques and it depends on the given generators of $I$.
Tijdschrift: Journal of Computational and Applied Mathematics
ISSN: 0377-0427
Volume: 342
Pagina's: 119 - 132
Jaar van publicatie:2018