Improved two-step Newton’s method for computing simple multiple zeros of polynomial systems

Autor: Nan Li, Lihong Zhi

Publikováno v: Numerical Algorithms. 91:19-50

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e76ac06d6b9f260fe24d847a7279ca09
https://doi.org/10.1007/s11075-022-01253-7

Lifts of Non-Compact Convex Sets and Cone Factorizations

Autor: Lihong Zhi, Chu Wang

Publikováno v: Journal of Systems Science and Complexity. 33:1632-1655

This paper generalizes the factorization theorem of Gouveia, Parrilo and Thomas to a broader class of convex sets. Given a general convex set, the authors define a slack operator associated to the set and its polar according to whether the convex set

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::580a07d5011130a3741271470705d247
https://doi.org/10.1007/s11424-020-9050-y

Global Optimization of Polynomials over Real Algebraic Sets

Autor: Lihong Zhi, Zhi-Hong Yang, Chu Wang

Publikováno v: Journal of Systems Science and Complexity. 32:158-184

Let f, g1,..., gs be polynomials in R[X1,..., Xn]. Based on topological properties of generalized critical values, the authors propose a method to compute the global infimum f* of f over an arbitrary given real algebraic set V = {x ∈ Rn | g1(x) = 0

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::22ed95268b8eaa7bdc4a8fa24ebb7b5b
https://doi.org/10.1007/s11424-019-8351-5

A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals

Autor: Lihong Zhi, Chu Wang, Yue Ma

Publikováno v: Journal of Symbolic Computation. 72:1-20

For an ideal I with a positive-dimensional real variety V R ( I ) , based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Grobner basis of an ideal J generated by the kernel of a truncated moment matrix and s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ba522f3b3b465fa38332dd527427152f
https://doi.org/10.1016/j.jsc.2014.12.002

On the complexity of computing real radicals of polynomial systems

Autor: Zhi-Hong Yang, Mohab Safey El Din, Lihong Zhi

Publikováno v: ISSAC '18-The 2018 ACM on International Symposium on Symbolic and Algebraic Computation
ISSAC '18-The 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Jul 2018, New-York, United States. pp.351-358, ⟨10.1145/3208976.3209002⟩
ISSAC

International audience; Let f= (f1, ..., fs) be a sequence of polynomials in Q[X1,...,Xn] of maximal degree D and V⊂ Cn be the algebraic set defined by f and r be its dimension. The real radical re < f > associated to f is the largest ideal which d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29d4fdef172d9f5a93e981825baef2ee
https://hal.inria.fr/hal-01956596/file/SaYaZhi18.pdf