# A note on geometric involutive bases for positive dimensional polynomial ideals and SDP methods

@inproceedings{Reid2014ANO, title={A note on geometric involutive bases for positive dimensional polynomial ideals and SDP methods}, author={Gregory J. Reid and Fei Wang and Wenyuan Wu}, booktitle={SNC}, year={2014} }

This paper is motivated by [1] which gives a new symbolic-numeric approach for computing the real radical of zero dimensional polynomial systems using geometric involution and semi-definite programming (SDP) techniques. We explore the interplay between geometric involutive bases and the new SDP methods in the positive dimensional case. An important work on this topic is [5].

## 5 Citations

Facial Reduction and SDP Methods for Systems of Polynomial Equations

- MathematicsArXiv
- 2015

A framework for combining facial reduction with such SDP methods for analyzing $0$ and positive dimensional real ideals of real polynomial systems is introduced and the geometric involutive form is implemented in Maple.

Semidefinite Programming and facial reduction for 1 Systems of Polynomial Equations

- Mathematics
- 2015

6 For a real polynomial system with finitely many complex roots, the 7 real radical ideal, RRI, is generated by a lower degree system that has 8 only real roots and the roots are free of…

Computing the generators of the truncated real radical ideal by moment matrices and SDP facial reduction

- Mathematics, Computer Science
- 2016

A method to compute the generators of the real radical for any given degree $d$, which combines the use of moment matrices and techniques from SDP optimization: facial reduction first developed by Borwein and Wolkowicz.

Computation of Real Radical Ideals by Semidefinite Programming and Iterative Methods

- Mathematics, Computer Science
- 2016

A contribution of the thesis is to show how to apply facial reduction pioneered by Borwein and Wolkowicz to this problem, which is proved to be stable under some assumptions as the max rank doesn’t change under sufficiently small perturbations.

Finding Maximum Rank Moment Matrices by Facial Reduction and Douglas-Rachford Method on Primal Form

- Computer Science, Mathematics
- 2016

How to compute the moment matrix and its kernel using facial reduction techniques where the maximum rank property can be guaranteed by solving the dual problem is discussed.

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