{"id":77,"date":"2014-11-28T15:17:46","date_gmt":"2014-11-28T14:17:46","guid":{"rendered":"https:\/\/project.inria.fr\/singcast\/?page_id=77"},"modified":"2014-12-18T17:46:07","modified_gmt":"2014-12-18T16:46:07","slug":"nantes-20141214-15-methodes-de-subdivisions-pour-les-systemes-singuliers","status":"publish","type":"page","link":"https:\/\/project.inria.fr\/singcast\/reunions\/nantes-20141214-15-methodes-de-subdivisions-pour-les-systemes-singuliers\/","title":{"rendered":"NANTES 2014\/12\/15-16 M\u00e9thodes de subdivisions pour les syst\u00e8mes singuliers"},"content":{"rendered":"<style><!--\n a.tooltip {outline:none; }\na.tooltip strong {line-height:30px;}\na.tooltip:hover {text-decoration:none;}\na.tooltip span {\nz-index:10;display:none; padding:14px 20px;\nmargin-top:-30px; margin-left:28px;\nwidth:300px; line-height:16px;\n}\na.tooltip:hover span{\ndisplay:inline; position:absolute; color:#111;\nborder:1px solid #DCA; background:#fffAF0;}\n.callout {z-index:20;position:absolute;top:30px;border:0;left:-12px;}\n\n\/*CSS3 extras*\/\na.tooltip span\n{\nborder-radius:4px;\nbox-shadow: 5px 5px 8px #CCC;\n}\n--><\/style>\n<h1>Programme<\/h1>\n<ul>\n<li><strong>Lundi 15 matin : Robotique<\/strong>\n<ul>\n<li>9h30 Accueil<\/li>\n<li>10h St\u00e9phane Caro, CARO,   <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/141215_JourneesSingularites_StephaneCARO.pdf\">Singularit\u00e9s parall\u00e8les des robots parall\u00e8les<\/a><\/li>\n<li>10h30 Damien Chablat, <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/2014_Chablat_Singularit\u00e9s.pdf\">\u00c9tude du robot 3-RPS : R\u00e9sultats et limitations des outils alg\u00e9briques <\/a><\/li>\n<li>11h Gilles Chabert , <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/gillles_chabertsingcast.pdf\">IBEX<\/a><a class=\"tooltip\" href=\"#\">  Abstract <span> <strong>Abstract<\/strong><br \/>\nNous commencerons par donner un rapide tour d&rsquo;horizon de la librairie Ibex. Cette libraire \u00e9tant orient\u00e9e \u00ab\u00a0contracteur\u00a0\u00bb, nous insisterons en particulier sur cette notion. Dans un second temps, nous donnerons un exemple d&rsquo;utilisation concret: nous montrerons comment int\u00e9grer un contracteur sp\u00e9cifique dans Ibex et le combiner avec ceux fournis par d\u00e9faut dans la librairie. L&rsquo;exemple que nous prendrons sera tout simplement l&rsquo;intersection de deux cercles c1 et c2 dans le plan. Plut\u00f4t que de mettre en s\u00e9quence des algorithmes de contraction de type forward-backward ou Newton intervalle sur les \u00e9quations du cercle, il est possible de donner une formule explicite pour les deux points d&rsquo;intersection. Cependant, celle-ci n\u00e9cessite de prendre en compte les diff\u00e9rentes valeurs possible du signe d&rsquo;un discriminant. Il est donc plus commode d&rsquo;\u00e9crire directement un algorithme et de voir la relation x=inter(c1,c2) comme un contracteur d\u00e9di\u00e9.  Nous montrerons comment \u00e9crire ce contracteur en C++ et le combiner avec les autres.<\/span><\/a><\/li>\n<\/ul>\n<\/li>\n<li><strong>Lundi 15 aprem : M\u00e9thodes num\u00e9riques<\/strong>\n<ul>\n<li>14h30 Stef Graillat, <a class=\"tooltip\" href=\"#\"> Verified error bounds for multiple roots of systems of nonlinear equations <span> <strong>Abstract<\/strong><br \/>\nIt is well known that it is an ill-posed problem to decide whether a function has a multiple root. Even for a univariate polynomial an arbitrary small perturbation of a polynomial coefficient may change the answer from yes to no. Let a system of nonlinear equations be given. In this talk, we will describe an algorithm for computing verified and narrow error bounds with the property that a slightly perturbed system is proved to have a double root within the computed bounds. For a univariate nonlinear function, we will give a similar method also for a multiple root. A narrow error bound for the perturbation is computed as well. Computational results for systems with up to 1000 unknowns demonstrate the performance of the methods. This is a joint work with Prof. Siegfried M. Rump. <\/span><\/a>   <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/slides-stef.pdf\">(slides)<\/a><\/li>\n<li>15h00 Alexandre Goldsztejn , <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/alex.pdf\">Certified parallelotope continuation for one-manifolds<\/a><\/li>\n<li>15h30-18h Discussions, probl\u00e8mes de robotique<\/li>\n<li>19h30 Diner \u00e0 <a title=\"La Cigale\" href=\"http:\/\/www.lacigale.com\/\" target=\"_blank\">La Cigale<\/a>, 4, place Graslin (face \u00e0 l\u2019Op\u00e9ra), (veillez \u00e0 etre \u00e0 l&rsquo;heure car il y a 2 services le soir, merci!)<\/li>\n<\/ul>\n<\/li>\n<li><strong>Mardi 16 matin: M\u00e9thodes alg\u00e9brico-num\u00e9rique<\/strong>\n<ul>\n<li>9h30 Nicolas Delanoue, <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/delanoue.pdf\">Contour apparent d&rsquo;applications lisses de R^2 dans R^2 via le calcul par intervalles<\/a><\/li>\n<li>10h Guillaume Moroz, Projection of smooth curves and silhouettes with subresultant<br \/>\n<a class=\"tooltip\" href=\"#\"> Numeric certified algorithm for the topology of resultant and discriminant curves <span> <strong>Abstract<\/strong>Let C be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfacesP(x,y,z)=Q(x,y,z)=0 (resp. P(x,y,z)=\u2202P\/\u2202z(x,y,z)=0),and generically its singularities are nodes (resp. nodes and ordinary cusp).State-of-the-art numerical algorithms cannot handle the computation of its topology. The main challenge is to find numerical criteria that guarantee the existence and the uniqueness of a singularity inside a given box B, while ensuring that B does not contain any closed loop of C. We solve this problem by providing a square deflation system that can be used to certify numerically whether B contains a singularity p. Then we introduce a numeric adaptive separation criterion based on interval arithmetic to ensure that the topology of C in B is homeomorphic to the local topology at p.<\/span><\/a><br \/>\n<a href=\"http:\/\/archivesic.ccsd.cnrs.fr\/INRIA-LORRAINE-LORIA-SET\/hal-01093040v1\">Preprint<\/a> <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/topologie_discriminant.pdf\">slides<\/a>\n<\/li>\n<li>10h30 Romain Benoit, <a href=\"https:\/\/project.inria.fr\/singcast\/files\/2014\/12\/benoit-romain.pdf\">Objets combinatoires et invariants de fonctions lisses. Applications \u00e0 la robotique<\/a><\/li>\n<li> Discussions, <\/li>\n<\/ul>\n<\/li>\n<li><strong>Mardi 16 aprem<\/strong><\/li>\n<ul>\n<li> 14h-16h Discussions <\/li>\n<\/ul>\n<\/ul>\n<h1>Probl\u00e8mes ouverts<\/h1>\n<p><a target=\"_blank\" title=\"pad\" href=\"https:\/\/pad.inria.fr\/p\/g.HW1VzvWSVAyJkMQn$CXiUGa5mkX3BNJ76_singcast-open-pb\">Document en ligne avec password pour probl\u00e8mes ouverts:<\/a><\/p>\n<h1>Lieu de la r\u00e9union<\/h1>\n<p>IRCCyN, Salle S018, Arret de tram 2: \u00ab\u00a0\u00c9cole Centrale-Audencia\u00a0\u00bb, puis suivre l&rsquo;itin\u00e9raire bleu dans le campus (voir la carte).<br \/>\n<iframe loading=\"lazy\" src=\"https:\/\/www.google.com\/maps\/embed?pb=!1m29!1m12!1m3!1d2454.417141504782!2d-1.5518551021246458!3d47.24939937685482!2m3!1f0!2f0!3f0!3m2!1i1024!2i768!4f13.1!4m14!1i1!3e6!4m5!1s0x4805ee64b6aad751%3A0x236ca335739d322!2s%C3%89cole+Centrale-Audencia%2C+France!3m2!1d47.248636!2d-1.551184!4m5!1s0x4805ee6434bae091%3A0xeb4de3c71e542bee!2sIRCCyN%2C+44300+Nantes%2C+France!3m2!1d47.250164!2d-1.547399!5e1!3m2!1sen!2sus!4v1417448505967\" width=\"600\" height=\"450\" frameborder=\"0\" style=\"border:0\"><\/iframe><\/p>\n<h1>Hotel et restaurant<\/h1>\n<ul>\n<li> <a href=\"http:\/\/www.hotel-chateaubriand-nantes.fr\/\">Hotel Chateaubriand<\/a>, 2 bis Rue Ch\u00e2teaubriand, 44000 Nantes <\/li>\n<li>19h30 Diner \u00e0 <a title=\"La Cigale\" href=\"http:\/\/www.lacigale.com\/\" target=\"_blank\">La Cigale<\/a>, 4, place Graslin (face \u00e0 l\u2019Op\u00e9ra), (veillez \u00e0 etre \u00e0 l&rsquo;heure car il y a 2 services le soir, merci!)<\/li>\n<\/ul>\n<p><a href=\"https:\/\/www.google.com\/maps\/d\/edit?mid=zYZKJ6w43lr0.kPnbcO7UrWFg\">Carte hotel, restaurant et IRRCyN<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Programme Lundi 15 matin : Robotique 9h30 Accueil 10h St\u00e9phane Caro, CARO, Singularit\u00e9s parall\u00e8les des robots parall\u00e8les 10h30 Damien Chablat, \u00c9tude du robot 3-RPS : R\u00e9sultats et limitations des outils alg\u00e9briques 11h Gilles Chabert , IBEX Abstract Abstract Nous commencerons par donner un rapide tour d&rsquo;horizon de la librairie Ibex. Cette libraire \u00e9tant orient\u00e9e \u00ab\u00a0contracteur\u00a0\u00bb, &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/project.inria.fr\/singcast\/reunions\/nantes-20141214-15-methodes-de-subdivisions-pour-les-systemes-singuliers\/\">Lire la suite<\/a><\/p>\n","protected":false},"author":584,"featured_media":0,"parent":72,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-77","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/pages\/77","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/users\/584"}],"replies":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/comments?post=77"}],"version-history":[{"count":56,"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/pages\/77\/revisions"}],"predecessor-version":[{"id":148,"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/pages\/77\/revisions\/148"}],"up":[{"embeddable":true,"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/pages\/72"}],"wp:attachment":[{"href":"https:\/\/project.inria.fr\/singcast\/wp-json\/wp\/v2\/media?parent=77"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}