A Sum of Squares Approximation of Nonnegative Polynomials

Authors:
Jean B. Lasserre
Affiliations:
-
Venue:
SIAM Review
Year:
2007

Citing 0
Cited 6

Faster real feasibility via circuit discriminants

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Neural Network Control of Unknown Nonlinear Systems with Efficient Transient Performance

ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Control of unknown nonlinear systems with efficient transient performance using concurrent exploitation and exploration

IEEE Transactions on Neural Networks
Coupling policy iteration with semi-definite relaxation to compute accurate numerical invariants in static analysis

ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
Random Graphons and a Weak Positivstellensatz

Journal of Graph Theory
Maximum Block Improvement and Polynomial Optimization

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that every real nonnegative polynomial $f$ can be approximated as closely as desired (in the $l_1$-norm of its coefficient vector) by a sequence of polynomials $\{f_\epsilon\}$ that are sums of squares. The novelty is that each $f_\epsilon$ has a simple and explicit form in terms of $f$ and $\epsilon$.