# The singular value decomposition for approximate polynomial systems

@inproceedings{Corless1989TheSV, title={The singular value decomposition for approximate polynomial systems}, author={Robert M Corless and Patrizia M. Gianni and Barry M. Trager and Stephen M. Watt}, booktitle={ISSAC 1989}, year={1989} }

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## 4 Citations

A Fast Algorithm for Approximate Polynomial GCD Based on Structured Matrix Computations

- Computer Science
- 2010

Numerical experiments performed with a wide variety of test problems, show the effectiveness of this algorithm in terms of speed, stability and robustness, together with its better reliability with respect to the available software.

Extended companion matrix for approximate GCD

- Mathematics, Computer ScienceSNC '11
- 2012

The structure of the null space of the multiplication matrix contains all the essential information about GCD(f, g) and exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.

Structured matrix-based methods for polynomial ∈-gcd: analysis and comparisons

- Computer Science, MathematicsISSAC '07
- 2007

The main result is the design of a practically stable algorithm whose arithmetic cost is quadratic in the degrees of the input polynomials.

A numerical absolute primality test for bivariate polynomials

- MathematicsISSAC
- 1997

This work gives a new numerical absolute primality criterion for bivariate polynomials based on a simple property of the monomials appearing after a generic linear change of coordinates and provides a probabilistic algorithm for detecting absolute factors.