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Research
Centre Scientific Computing: Applied Linear Algebra
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2013 - Autumn semester December 26, 11:00 AM, Room #60 December 12, 11:00 AM, Room #60 In this talk we consider an attempt to classify finite homomorphism-homogeneous algebraic systems. We first characterize homomorphism-homogeneous monounary algebras (joint work with Éva Jungábel), and then show that deciding whether a finite algebraic system with at least one at least binary operation is homomorphism-homogeneous is a coNP-complete problem. The hardness of this problem follows by a technically rather involved interpretation of finite graphs in terms of finite algebraic systems, and a recent result of Rusinov and Schweitzer that deciding whether a finite graph with loops is homomorphism-homogeneous is a coNP-complete problem. We close the talk with a dichotomy conjecture (deciding whether a finite algebraic system is homomorphism-homogeneous is either in P or coNP-complete) and an open problem that would lead to the proof of the conjecture. November 28, 11:00 AM, Room #60 We study (1 : b) Avoider-Enforcer games played on the edge set of the complete graph on n vertices. For every constant k≥3 we analyse the k-star game, where Avoider tries to avoid claiming k edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games - the strict and the monotone - and for each provide explicit winning strategies for both players. Consequentially, we establish bounds on the threshold biases fFmon, fF- and fF+, where F is the hypergraph of the game. We also study three related monotone games. This is joint work with Andrzej Grzesik, Zoltán Lóránt Nagy, Alon Naor, Balázs Patkós and Fiona Skerman. November 21, 11:00 AM, Room #60 November 14, 11:00 AM, Room #60 It is well known that non-singularity of one special class of matrices, named SDD matrices, is at its core analogous with the principles established in the classical Geršgorin theorem. Moreover, the concept of SDD matrix non-singularity is firmly based on the grounds of maximum matrix norm. Although direct switch to other norm may not result in significant overall benefits right from the start, Euclidean norm approach led to some compelling outcomes. The focus of our work is to induce this concept to some other class of H-matrices, especially to those of S-SDD and alpha type, and discuss plausible benefits concerning problems in various fields of applied linear algebra. November 7, 11:00 AM, Room #60 I will repeat my invited plenary lecture from the GAIA 2013 conference in Melbourne, Australia, held in July 2013. The full abstract can be downloaded by clicking here. October 31, 11:00 AM, Room #60 Quadratic eigenvalue problems appear in many applications, and the research concerning their proper treatment has drawn a lot of attention in the past few years. In some cases, however, exact computation of eigenvalues is not necessary, while their position or distribution in the complex plane is of importance. To address such situations, in this talk we will present localization techniques for quadratic eigenvalue problems that are based on the use of strictly diagonal dominant matrices. In addition, we will prove some useful properties of the obtained localization areas, and illustrate them through numerical examples. October 24, 11:00 AM, Room #60 Motivated by recent papers on max-norm bounds of the inverse of a matrix that belongs to a certain subclass of H-matrices, we obtain a new non-singularity result as a generalization of the Nekrasov property. Also, we present new max-norm bounds for the inverse matrix and illustrate these results by numerical examples. October 17, 11:00 AM, Room #60 |
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