The singular value decomposition for polynomial systems
@inproceedings{Corless1995TheSV, title={The singular value decomposition for polynomial systems}, author={Robert M Corless and P. Gianni and Barry M. Trager and S. Watt}, booktitle={ISSAC '95}, year={1995} }
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coecients 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 ecient 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… CONTINUE READING
Figures and Topics from this paper
Figures
231 Citations
Approximate factorization of multivariate polynomials using singular value decomposition
- Mathematics, Computer Science
- J. Symb. Comput.
- 2008
- 66
- PDF
Approximate factorization of multivariate polynomials via differential equations
- Mathematics, Computer Science
- ISSAC '04
- 2004
- 84
- PDF
The approximate irreducible factorization of a univariate polynomial: revisited
- Mathematics, Computer Science
- ISSAC '09
- 2009
- 9
NUMERICAL ALGEBRAIC GEOMETRY: THE CANONICAL DECOMPOSITION AND NUMERICAL GR OBNER BASES
- Mathematics
- 2012
- 2
Computing Lower Rank Approximations of Matrix Polynomials
- Mathematics, Computer Science
- J. Symb. Comput.
- 2020
- 1
- Highly Influenced
- PDF
An ODE-based method for computing the approximate greatest common divisor of polynomials
- Mathematics, Computer Science
- Numerical Algorithms
- 2018
- 7
- PDF
On Approximate GCDs of Univariate Polynomials
- Computer Science, Mathematics
- J. Symb. Comput.
- 1998
- 104
- PDF
References
LAPACK User’s Guide
- 2nd. ed., SIAM
- 1995