This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an algorithm for computing univariate GCD's which gives exact results for interesting nearby problems, and give efficient algorithms for computing precisely how nearby. We generalize this to multivariate GCD computation. Next, we adapt Lazard's u-resultant algorithm for the solution of overdetermined systems of polynomial equations to the inexact-coefficient case. We also briefly discuss an application of the modified Lazard's method to the location of singular points on approximately known projections of algebraic curves.
Singular value decomposition for polynomial systems
GIANNI, PATRIZIA;
1995-01-01
Abstract
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an algorithm for computing univariate GCD's which gives exact results for interesting nearby problems, and give efficient algorithms for computing precisely how nearby. We generalize this to multivariate GCD computation. Next, we adapt Lazard's u-resultant algorithm for the solution of overdetermined systems of polynomial equations to the inexact-coefficient case. We also briefly discuss an application of the modified Lazard's method to the location of singular points on approximately known projections of algebraic curves.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
