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Prof. Dr. Michael Stiebitz

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Publications

Publications at the institute since 1990

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Giribet, Juan; Langer, Matthias; Martínez Pería, Francisco; Philipp, Friedrich; Trunk, Carsten;
Spectral enclosures for a class of block operator matrices. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (23 Seiten). . - (Preprint. - M19,04)

We prove new spectral enclosures for the non-real spectrum of a class of 2x2 block operator matrices with self-adjoint operators A and D on the diagonal and operators B and -B* as off-diagonal entries. One of our main results resembles Gershgorin's circle theorem. The enclosures are applied to J-frame operators.



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200198
Ilchmann, Achim; Leben, Leslie; Witschel, Jonas; Worthmann, Karl;
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods. - New York, NY [u.a.] : Wiley, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366

https://doi.org/10.1002/oca.2481
Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia;
Using a B&B algorithm from multiobjective optimization to solve constrained optimization problems. - In: AIP conference proceedings. - Melville, NY : Inst, ISSN 15517616, Bd. 2070 (2019), S. 020028, insges. 4 S.

https://doi.org/10.1063/1.5089995
Schweser, Thomas; Stiebitz, Michael;
Partitions of multigraphs under minimum degree constraints. - In: Discrete applied mathematics. - [S.l.] : Elsevier, Bd. 257 (2019), S. 269-275

https://doi.org/10.1016/j.dam.2018.10.016
Schlipf, Lena; Schmidt, Jens M.;
Simple computation of st-edge- and st-numberings from ear decompositions. - In: Information processing letters : devoted to the rapid publication of short contributions to information processing.. - Amsterdam [u.a.] : Elsevier, ISSN 1872-6119, Bd. 145 (2019), S. 58-63

https://doi.org/10.1016/j.ipl.2019.01.008
Gernandt, Hannes; Pade, Jan Philipp;
Schur reduction of trees and extremal entries of the Fiedler vector. - In: Linear algebra and its applications : LAA.. - New York, NY : American Elsevier Publ., Bd. 570 (2019), S. 93-122

https://doi.org/10.1016/j.laa.2019.02.008
Gernandt, Hannes; Moalla, Nedra; Philipp, Friedrich; Selmi, Wafa; Trunk, Carsten;
Invariance of the essential spectra of operator pencils. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (15 Seiten). . - (Preprint. - M19,03)

The essential spectrum of operator pencils with bounded coefficients in a Hilbert space is studied. Sufficient conditions in terms of the operator coefficients of two pencils are derived which guarantee the same essential spectrum. This is done by exploiting a strong relation between an operator pencil and a specific linear subspace (linear relation).



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200141
Kriesell, Matthias; Mohr, Samuel;
Rooted complete minors in line graphs with a Kempe coloring. - In: Graphs and combinatorics. - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 35 (2019), 2, S. 551-557

https://doi.org/10.1007/s00373-019-02012-7
Cao, Yan; Chen, Guantao; Jing, Guangming; Stiebitz, Michael; Toft, Bjarne;
Graph edge coloring: a survey. - In: Graphs and combinatorics. - Tokyo : Springer-Verl. Tokyo, ISSN 1435-5914, Bd. 35 (2019), 1, S. 33-66

https://doi.org/10.1007/s00373-018-1986-5
Leben, Florian; Trunk, Carsten;
Operator based approach to PT-symmetric problems on a wedge-shaped contour. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2019. - 1 Online-Ressource (23 Seiten). . - (Preprint. - M19,02)

We consider a second-order differential equation -y''(z)-(iz)^{N+2}y(z)=\lambda y(z), z\in \Gamma with an eigenvalue parameter \lambda \in C. In PT quantum mechanics z runs through a complex contour \Gamma in C, which is in general not the real line nor a real half-line. Via a parametrization we map the problem back to the real line and obtain two differential equations on [0,\infty) and on (-\infty,0]. They are coupled in zero by boundary conditions and their potentials are not real-valued. The main result is a classification of this problem along the well-known limit-point/ limit-circle scheme for complex potentials introduced by A.R. Sims 60 years ago. Moreover, we associate operators to the two half-line problems and to the full axis problem and study their spectra.



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2019200020