VeranstaltungsortI.2.01Veranstalter Institut für MathematikBeschreibungAt the beginning of the talk I will give a short speech on what is a inverse problem and how to come up with the Iteratively Regularized Gauss Newton Method (IRGNM). This talk deals with an analysis of IRGNM in its Ivanov version in a Banach space setting; the Ivanov version is an equivalent formulation to the Tikhonov version but with a restriction on the minimization process instead of a penalty on the cost function as in Tikhonov. The choice of parameter regularization play crucial roles in all methods to solve a inverse problem; since parameters chosen in a priori fashion might depend on some knowledge of the solution, we present here a posteriori choice of parameter. I will show convergence results in its continuous and discretized version. At the end, I present a model example and show how is the IRGNM step and how to solve it.Vortragende(r)Mario Previatti de SouzaKontaktSenka Haznadar (senka.omerhodzic@aau.at)

VeranstaltungsortAlpen-Adria-Universität KlagenfurtI.2.01Veranstalter Institut für MathematikBeschreibungThe f-vector of a d-dimensional (convex) polytope P is defined as f(P) = (f_0(P), f_1(P), ... , f_d(P)) where f_i(P) is the number of i-dimensional faces of P.The question is whether a given vector of non-negative numbers is the f-vector of a polytope.For d >= 4, finding a complete characterization of f-vectors is an open problem.However, the so-called g-Theorem gives a description for f-vectors of simplicial and simple polytopes. The purpose of this talk is to give a summary of the lectures of a summer school at MSRI on the g-Theorem and related topics.Vortragende(r)Roswitha RissnerKontaktSenka Haznadar (senka.omerhodzic@aau.at)