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The Geometry of Multivariate Polynomial Division and Elimination

Author:
Batselier, Kim   Dreesen, Philippe   Moor, Bart De  


Journal:
SIAM Journal on Matrix Analysis and Applications


Issue Date:
2013


Abstract(summary):

Multivariate polynomials are usually discussed in the framework of algebraic geometry. Solving problems in algebraic geometry usually involves the use of a Grobner basis. This article shows that linear algebra without any Grobner 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.


Page:
102-125


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