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Prof. Dr. rer. nat. habil. Matthias Kriesell


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Veröffentlichungen am Institut für Mathematik seit 1990

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Behrndt, Jussi; Möws, Roland; Trunk, Carsten;
Eigenvalue estimates for operators with finitely many negative squares. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (14 Seiten). . - (Preprint. - M16,02)

Let A and B be selfadjoint operators in a Krein space. Assume that the re- solvent difference of A and B is of rank one and that the spectrum of A consists in some interval I of isolated eigenvalues only. In the case that A is an operator with finitely many negative squares we prove sharp estimates on the number of eigenvalues of B in the interval I. The general results are applied to singular indefinite Sturm-Liouville problems.
Harant, Jochen; Mohr, Samuel;
Maximum weighted induced subgraphs. - In: Discrete mathematics. - Amsterdam [u.a.] : Elsevier, Bd. 339 (2016), 7, S. 1954-1559
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen;
On contractual periods in supplier development. - In: IFAC-PapersOnLine. - Frankfurt : Elsevier, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65
Axenovich, Maria; Harant, Jochen; Przybyło, Jaromir; Soták, Roman; Voigt, Margit; Weidelich, Jenny;
A note on adjacent vertex distinguishing colorings of graphs. - In: Discrete applied mathematics. - [S.l.] : Elsevier, Bd. 205 (2016), S. 1-7
Behrndt, Jussi; Leben, Leslie; Martínez Pería, Francisco; Möws, Roland; Trunk, Carsten;
Sharp eigenvalue estimates for rank one perturbations of nonnegative operators in Krein spaces. - In: Journal of mathematical analysis and applications. - Amsterdam [u.a.] : Elsevier, Bd. 439 (2016), 2, S. 864-895
Gernandt, Hannes; Trunk, Carsten;
Eigenvalue placement for regular matrix pencils with rank one perturbations. - Ilmenau : Technische Universität, Institut für Mathematik, 2016. - 1 Online-Ressource (15 Seiten). . - (Preprint. - M16,01)

A regular matrix pencil sE-A and its rank one perturbations are considered. We determine the sets in \C\cup\{\infty\} which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE-A may disappear and the sum of the length of all destroyed Jordan chains is the number of eigenvalues (counted with multiplicities) which can be placed arbitrarily in \C\cup\{\infty\}. We prove sharp upper and lower bounds of the change of the algebraic and geometric multiplicity of an eigenvalue under rank one perturbations. Finally we apply our results to a pole placement problem for a single-input differential algebraic equation with feedback.
Eichfelder, Gabriele; Gerlach, Tobias; Sumi, Susanne;
A modification of the [alpha]BB method for box-constrained optimization and an application to inverse kinematics. - In: EURO journal on computational optimization. - Berlin : Springer, ISSN 2192-4414, Bd. 4 (2016), 1, S. 93-121

For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information which cannot be formulated as a mathematical function or within a hierarchical problem formulation. We present such an application in the field of robotic design. This application problem can be modeled as a smooth box-constrained optimization problem. We extend the well-known alphaBB method such that it can be used to find an approximation of the set of globally optimal solutions with a predefined quality. We illustrate the properties and give a proof for the finiteness and correctness of our modified alphaBB method.
Knobloch, Jürgen; Vielitz, Martin
Non-conservative perturbations of homoclinic snaking scenarios. - In: Journal of differential equations. - Orlando, Fla. : Elsevier, ISSN 1090-2732, Bd. 260 (2016), 1, S. 517-566
Berger, Thomas; Trunk, Carsten; Winkler, Henrik
Linear relations and the Kronecker canonical form. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 488 (2016), S. 13-44
Brás, Carmo; Eichfelder, Gabriele; Júdice, Joaquim;
Copositivity tests based on the linear complementarity problem. - In: Computational optimization and applications : an international journal.. - New York, NY [u.a.] : Springer Science + Business Media B.V., ISSN 1573-2894, Bd. 63 (2016), 2, S. 164-493

We present copositivity tests based on new necessary and sufficient conditions which require the solution of linear complementarity problems (LCP). We propose methodologies involving Lemkes method, an enumerative algorithm and a linear mixed-integer programming formulation to solve the required LCPs. Moreover, we discuss a new necessary condition for (strict) copositivity based on solving a linear program, which can be used as a preprocessing step. The algorithms with these three different variants are thoroughly applied to test matrices from the literature and to max-clique instances with matrices of order up to 496×496. We compare our procedures with three other copositivity tests from the literature as well as with a general global optimization solver. The numerical results are very promising and equally good and in many cases better than the results reported elsewhere.