Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773155 | Linear Algebra and its Applications | 2017 | 20 Pages |
Abstract
For a square-free bivariate polynomial p of degree n we introduce a simple and fast numerical algorithm for the construction of nÃn matrices A, B, and C such that detâ¡(A+xB+yC)=p(x,y). This is the minimal size needed to represent a bivariate polynomial of degree n. Combined with a square-free factorization one can now compute nÃn matrices for any bivariate polynomial of degree n. The existence of such symmetric matrices was established by Dixon in 1902, but, up to now, no simple numerical construction has been found, even if the matrices can be nonsymmetric. Such representations may be used to efficiently numerically solve a system of two bivariate polynomials of small degree via the eigenvalues of a two-parameter eigenvalue problem. The new representation speeds up the computation considerably.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Bor Plestenjak,