A divide-and-conquer algorithm for computing Gröbner bases of syzygies in finite dimension

Autor: Simone Naldi, Vincent Neiger

Publikováno v: ISSAC

Let $f_1,\ldots,f_m$ be elements in a quotient $R^n / N$ which has finite dimension as a $K$-vector space, where $R = K[X_1,\ldots,X_r]$ and $N$ is an $R$-submodule of $R^n$. We address the problem of computing a Gr\"obner basis of the module of syzy

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::82ca9f60a211a4440dee4a5ebc2b70a8
https://hal-unilim.archives-ouvertes.fr/hal-02480240v2/document

Real root finding for low rank linear matrices

Autor: Simone Naldi, Mohab Safey El Din, Didier Henrion

Publikováno v: Applicable Algebra in Engineering, Communication and Computing
Applicable Algebra in Engineering, Communication and Computing, 2020, 31, pp.101-133. ⟨10.1007/s00200-019-00396-w⟩
Applicable Algebra in Engineering, Communication and Computing, Springer Verlag, 2020, 31, pp.101-133. ⟨10.1007/s00200-019-00396-w⟩

We consider $m \times s$ matrices (with $m\geq s$) in a real affine subspace of dimension $n$. The problem of finding elements of low rank in such spaces finds many applications in information and systems theory, where low rank is synonymous of struc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::33acdc8ff3dd1c17063445c8bfecdefb
https://hal.science/hal-01159210v2/document

Exact algorithms for semidefinite programs with degenerate feasible set

Autor: Didier Henrion, Mohab Safey El Din, Simone Naldi

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, Elsevier, 2021, 104, pp.942-959. ⟨10.1016/j.jsc.2020.11.001⟩
ISSAC 2018-43rd International Symposium on Symbolic and Algebraic Computation
ISSAC 2018-43rd International Symposium on Symbolic and Algebraic Computation, Jul 2018, New York City, United States. 17p., ⟨10.1145/3208976.3209022⟩
ISSAC
Journal of Symbolic Computation, 2021, 104, pp.942-959. ⟨10.1016/j.jsc.2020.11.001⟩
Journal of Symbolic Computation, Elsevier, 2018, 17p

Given symmetric matrices $A_0, A_1, \ldots, A_n$ of size $m$ with rational entries, the set of real vectors $x = (x_1, \ldots, x_n)$ such that the matrix $A_0 + x_1 A_1 + \cdots + x_n A_n$ has non-negative eigenvalues is called a spectrahedron. Minim

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dc6bd0f05839f76df5e3f8010ab6f6e0
http://arxiv.org/abs/1802.02834

Exact algorithms for linear matrix inequalities

Autor: Mohab Safey El Din, Simone Naldi, Didier Henrion

Publikováno v: SIAM Journal on Optimization
SIAM Journal on Optimization, 2016, 26 (4), pp.2512-2539. ⟨10.1137/15M1036543⟩
SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 2016, 26 (4), pp.2512-2539. ⟨10.1137/15M1036543⟩

Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a convex sem

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6dfb4bf1a9f91e035483b4b78988bf1
https://hal.science/hal-01184320

Symbolic computation in hyperbolic programming

Autor: Daniel Plaumann, Simone Naldi

Publikováno v: Journal of Algebra and Its Applications
Journal of Algebra and Its Applications, World Scientific Publishing, 2018, 17 (10), pp.1850192. ⟨10.1142/S021949881850192X⟩

Hyperbolic programming is the problem of computing the infimum of a linear function when restricted to the hyperbolicity cone of a hyperbolic polynomial, a generalization of semidefinite programming. We propose an approach based on symbolic computati

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::38f3067e07ac2de548f01385246cb5ba