Zobrazeno 1 - 10
of 225
pro vyhledávání: '"Bernard Mourrain"'
Publikováno v:
Journal of Algebra
Journal of Algebra, 2022, 612, pp.691-721. ⟨10.1016/j.jalgebra.2022.08.026⟩
Journal of Algebra, 2022, 612, pp.691-721. ⟨10.1016/j.jalgebra.2022.08.026⟩
International audience; We address the description of the tropicalization of families of rational varieties under parametrizations with prescribed support, via curve valuations. We recover and extend results by Sturmfels, Tevelev and Yu for generic c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d7716c6324ecc192055eef68d8ea6d23
https://doi.org/10.1016/j.jalgebra.2022.08.026
https://doi.org/10.1016/j.jalgebra.2022.08.026
Autor:
Lorenzo Baldi, Bernard Mourrain
Publikováno v:
Mathematical Programming, Series A
Mathematical Programming, Series A, 2022, ⟨10.1007/s10107-022-01877-6⟩
Mathematical Programming, Series A, Springer, 2022, ⟨10.1007/s10107-022-01877-6⟩
Mathematical Programming, Series A, 2022, ⟨10.1007/s10107-022-01877-6⟩
Mathematical Programming, Series A, Springer, 2022, ⟨10.1007/s10107-022-01877-6⟩
We analyse the representation of positive polynomials in terms of Sums of Squares. We provide a quantitative version of Putinar's Positivstellensatz over a compact basic semialgebraic set S, with a new polynomial bound on the degree of the positivity
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd59073b690bc706d410e37378655d49
https://hal.science/hal-03437328v4/document
https://hal.science/hal-03437328v4/document
Publikováno v:
Journal of Symbolic Computation
Journal of Symbolic Computation, 2020, 101, pp.128-151. ⟨10.1016/j.jsc.2019.07.001⟩
Journal of Symbolic Computation, Elsevier, 2020, 101, pp.128-151. ⟨10.1016/j.jsc.2019.07.001⟩
Journal of Symbolic Computation, 2020, 101, pp.128-151. ⟨10.1016/j.jsc.2019.07.001⟩
Journal of Symbolic Computation, Elsevier, 2020, 101, pp.128-151. ⟨10.1016/j.jsc.2019.07.001⟩
International audience; We rely on aggregate separation bounds for univariate polynomials to introduce novel worst-case separation bounds for the isolated roots of zero-dimensional, positive-dimensional, and overde- termined polynomial systems. We ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::664971a2bb630aa49557091e7d9c7118
https://doi.org/10.1016/j.jsc.2019.07.001
https://doi.org/10.1016/j.jsc.2019.07.001
Autor:
Bernard Mourrain, Ibrahim Adamou
Publikováno v:
Mathematics in Computer Science
Mathematics in Computer Science, Springer, In press, ⟨10.1007/s11786-021-00508-1⟩
Mathematics in Computer Science, 2021, 15, pp.859-876. ⟨10.1007/s11786-021-00508-1⟩
Mathematics in Computer Science, Springer, In press, ⟨10.1007/s11786-021-00508-1⟩
Mathematics in Computer Science, 2021, 15, pp.859-876. ⟨10.1007/s11786-021-00508-1⟩
In this paper we consider the Voronoi diagram of a finite family of parallel half-lines, with the same orientation, constrained to a compact domain $${\mathscr {D}}_{0} \subset {\mathbb {R}}^3$$ , with respect to the Euclidean distance. We present an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e181f30aaa556a57020560128876f77
https://doi.org/10.1007/s11786-021-00508-1
https://doi.org/10.1007/s11786-021-00508-1
Autor:
Bernard Mourrain, Alessandro Oneto
Publikováno v:
Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩
Linear Algebra and its Applications, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩
Linear Algebra and its Applications, Elsevier, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩
Linear Algebra and its Applications, 2020, 607, pp.347-377. ⟨10.1016/j.laa.2020.06.029⟩
We use an algebraic approach to construct minimal decompositions of symmetric tensors with low rank. This is done by using Apolarity Theory and by studying minimal sets of reduced points apolar to a given symmetric tensor, namely, whose ideal is cont
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ce374a1f25a20e5143c7bccb5a486b7
https://doi.org/10.1016/j.laa.2020.06.029
https://doi.org/10.1016/j.laa.2020.06.029
Publikováno v:
Calcolo
Calcolo, 2022, ⟨10.1007/s10092-022-00484-3⟩
Calcolo, 2022, ⟨10.1007/s10092-022-00484-3⟩
This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c0633db43fc35008f3a6184a9708071
https://hal.archives-ouvertes.fr/hal-03390265/file/sn-article.pdf
https://hal.archives-ouvertes.fr/hal-03390265/file/sn-article.pdf
Publikováno v:
Journal of Computational Physics
Journal of Computational Physics, 2022, 466, pp.111393. ⟨10.1016/j.jcp.2022.111393⟩
Journal of Computational Physics, 2022, 466, pp.111393. ⟨10.1016/j.jcp.2022.111393⟩
International audience; Flux-aligned mesh generation plays an important role in the magnetohydrodynamic (MHD) simulation of Tokamak plasmas.In this paper, we present the existence theory of flux-aligned meshes by generalized Morse theory to the situa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ef8accf0451a53efed3e3f90649ad22
https://doi.org/10.1016/j.jcp.2022.111393
https://doi.org/10.1016/j.jcp.2022.111393
Publikováno v:
ACM Communications in Computer Algebra. 52:78-81
In this poster we present the results of [10]. We consider the problem of finding the common roots of a set of polynomial functions defining a zero-dimensional ideal I in a ring R of polynomials over C. We propose a general algebraic framework to fin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c178eb1baa82a9bf700a4a5c344f0984
https://doi.org/10.1145/3313880.3313888
https://doi.org/10.1145/3313880.3313888
Publikováno v:
Revista de la Union Matematica Argentina
Revista de la Union Matematica Argentina, 2022, 64 (2), pp.215-237. ⟨10.33044/revuma.2904⟩
Revista de la Union Matematica Argentina, 2022, 64 (2), pp.215-237. ⟨10.33044/revuma.2904⟩
Given rational univariate polynomials f and g such that gcd(f, g) and f / gcd(f, g) are relatively prime, we show that g is non-negative on all the real roots of f if and only if g is a sum of squares of rational polynomials modulo f. We complete our
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01da622cca9cde7281f2cdf399be2b7b
Autor:
Lorenzo Baldi, Bernard Mourrain
We investigate the problem of representing moment sequences by measures in the context ofPolynomial Optimization Problems. This consists in finding the infimum of a real polynomial ona real semialgebraic set defined by polynomial inequalities. We ana
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8e937fa05ca395acc6a5e78d5a34693
https://hal.archives-ouvertes.fr/hal-03082531
https://hal.archives-ouvertes.fr/hal-03082531