# On a condition number of general random polynomial systems

@article{Nguyen2016OnAC, title={On a condition number of general random polynomial systems}, author={Hoi H. Nguyen}, journal={Math. Comput.}, year={2016}, volume={85}, pages={737-757} }

Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of probability distributions. Our work also extends to certain perturbed systems.

## 5 Citations

### Probabilistic Condition Number Estimates for Real Polynomial Systems II: Structure and Smoothed Analysis

- MathematicsArXiv
- 2018

This work provides explicit estimates for condition numbers of structured random real polynomial systems, and extends these estimates to smoothed analysis setting, for sensitivity of real zeros to perturbations of their coefficients.

### Smoothed analysis for the condition number of structured real polynomial systems

- MathematicsMath. Comput.
- 2021

This work provides explicit estimates for condition numbers of structured random real polynomial systems, and extends these estimates to the smoothed analysis setting.

### Probabilistic Condition Number Estimates for Real Polynomial Systems I: A Broader Family of Distributions

- MathematicsFound. Comput. Math.
- 2019

The sensitivity of real roots of polynomial systems with respect to perturbations of the coefficients is considered and new probabilistic estimates are established that allow a much broader family of measures than considered earlier.

### Effects of singular value spectrum on the performance of echo state network

- Computer ScienceNeurocomputing
- 2019

### Sparsity, Randomness and Convexity in Applied Algebraic Geometry

- Mathematics, Computer Science
- 2016

The main theorem provides quantitative versions of some known algebraic facts, and also refines earlier quantitative results, on the condition number of polynomial systems ‘on average’, which is a vital invariant of poynomial systems which controls their computational complexity.

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