20 citations · 31 across the 23 of their papers we have counts for
4 papers · 1 filter
A certificate for semidefinite relaxations in computing positive dimensional real varieties
Yue Ma, Chu Wang, Lihong Zhi
For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal…
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
Nan Li, Lihong Zhi
In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on certifying breadth-one singular solutions of polynomial systems, to compu…
Certificates of Impossibility of Hilbert-Artin Representations of a Given Degree for Definite Polynomials and Functions
Feng Guo, Erich L. Kaltofen, Lihong Zhi
We deploy numerical semidefinite programming and conversion to exact rational inequalities to certify that for a positive semidefinite input polynomial or rational function, any re…
Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
Nan Li, Lihong Zhi
In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate…