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TitleThe geometry of multivariate polynomial division and elimination.
Author(s) Kim Batselier, Philippe Dreesen, Brian Moore
TypeArticle in Journal
AbstractMultivariate polynomials are usually discussed in the framework of algebraic geometry. Solving problems in algebraic geometry usually involves the use of a Gröbner basis. This article shows that linear algebra without any Gröbner basis computation suffices to solve basic problems from algebraic geometry by describing three operations: multiplication, division, and elimination. This linear algebra framework will also allow us to give a geometric interpretation. Multivariate division will involve oblique projections, and a link between elimination and principal angles between subspaces (CS decomposition) is revealed. The main computational tool in this approach is the QR decomposition.

ISSN0895-4798; 1095-7162/e
URL http://epubs.siam.org/doi/abs/10.1137/120863782
JournalSIAM J. Matrix Anal. Appl.
PublisherSociety for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
Translation No
Refereed No