Suzana Miodragović (Google Scholar Profile)

Associate Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-812
fax: +385-31-224-801
email:  ssusic @ mathos.hr
office:  14 (first floor)

 


Research Interests

Numerical Linear Algebra
Perturbation Theory
etc.

Degrees

PhD in theoretical mathematics, Department of Mathematics, University of Zagreb , 2014.
BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2007.
 

Publications

Journal Publications

  1. L. Grubišić, S. Miodragović, N. Truhar, Double angle theorems for definite matrix pairs, Electronic Transactions on Numerical Analysis 45 (2016), 33-57
    In this paper we present new double angle theorems for the rotation of the eigenspaces for Hermitian matrix pairs $(H,M)$, where $H$ is a non-singular matrix which can be factorized as $H = G J G^*$, $J = diag(pm 1)$, and $M$ is non-singular. The rotation of the eigenspaces is measured in the matrix dependent scalar product and the bounds belong to the relative perturbation theory. The quality of the new bounds are illustrated in the numerical examples.
  2. D. Jankov Maširević, S. Miodragović, Geometric median in the plane, Elemente der Mathematik 70 (2015), 21-32
  3. N. Truhar, S. Miodragović, Relative perturbation theory for de nite matrix pairs and hyperbolic eigenvalue problem, Applied Numerical Mathematics 98 (2015), 106-121
    In this paper, new relative perturbation bounds for the eigenvalues as well as for the eigensubspaces are developed for definite Hermitian matrix pairs and the quadratic hyperbolic eigenvalue problem. First, we derive relative perturbation bounds for the eigenvalues and the $sin Theta$ type theorems for the eigensubspaces of the definite matrix pairs $(A,B)$, where both $A, B in mathbb{C}^{mtimes m}$ are Hermitian nonsingular matrices with particular emphasis, where $B$ is a diagonal of $pm 1$. Further, we consider the following quadratic hyperbolic eigenvalue problem $(mu^2 M + mu C + K) x =0$, where $M, C, K in mathbb{C}^{ntimes n}$ are given Hermitian matrices. Using proper linearization and new relative perturbation bounds for definite matrix pairs $(A,B)$, we develop corresponding relative perturbation bounds for the eigenvalues and the $sin Theta$ type theorems for the eigensubspaces for the considered quadratic hyperbolic eigenvalue problem. The new bounds are uniform and depend only on matrices $M$, $C$, $K$, perturbations $delta M$, $delta C$ and $delta K$ and standard relative gaps. The quality of new bounds is illustrated through numerical examples.
  4. N. Truhar, L. Grubišić, S. Miodragović, The Rotation of Eigenspaces of Perturbed Matrix Pairs II, Linear and multilinear algebra 68/8 (2014), 1010-1031
    This paper studies the perturbation theory for spectral projections of Hermitian matrix pairs $(H, M)$, where $H$ is a non-singular Hermitian matrix which can be factorized as $H = G J G^*$, $J = diag(pm 1)$, and $M$ is positive definite. The class of allowed perturbations is so restricted that the corresponding perturbed pair $(wtd H, wtd M)= (H+delta H, M+ delta M)$ must have the form $wtd H = wtd G J wtd G^*$, $J = diag(pm 1)$ and $wtd M$ is positive definite. The main contribution of the paper is a $sinTheta$ theorem which generalizes the main result from the first part of the paper to this more general setting. Our estimate, in its most general form, depends on a uniform norm bound on a set of all $J$-unitary matrices which diagonalize $G^*G$. The second main contribution is a new sharp uniform estimate of a norm of all $J$-unitary matrices which diagonalize $G^*G$ such that $H=G^*JG$ is a quasi-definite matrix. The case of a quasi-definite pair is therefore the case where our bounds are most competitive. We present numerical experiments to corroborate the theory.



Projects


  • Project leader on Isolation of the unwanted part of the spectrum in the quadratic eigenvalue problem. Project was funded by J. J. Strossmayer University of Osijek, for period November, 2018.- May, 2020.
  • 01.07.2015. - 30.06.2019  investigator on scientific project "Optimization of parameter dependent mechanical systems (IP-2014-09-9540; OptPDMechSys). This project has been fully supported by Croatian Science Foundation
  • Mixed Integer Nonlinear Programming (MINLP) for damper optimization -- scientific project; supported by the DAAD for period 2015--2016 (investigator); cooperation with Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg
  • Investigator on Non-linear parameter dependent eigenvalue problem, project leader prof.dr.sc. Ninoslav Truhar. Project was funded by J. J. Strossmayer University of Osijek, for period 10.6.2016.-10.7.2016.
  • Optimzacija semi-aktivnog prigušenja kod titrajnih sistema, project leader: doc. dr. sc. Zoran Tomljanović, Deptartment of Mathematics, University of Osijek. Project was funded by J. J. Strossmayer University of Osijek, for period  2014.

 

 


Workshop and conference talk

 

  • GAMM ANLA Workshop Lund 2018, October, 10-12, 2018, Lund, Sweden
  • Eigensubspace perturbation bounds for quadratic eigenvalue problem, ApplMath18, September, 17-20, 2018, Šibenik, Croatia
  • Relative Perturbation Bounds for Hyperbolic Quadratic Eigenvalue Problem, 89th Annual Meeting of GAMM, March 19-23, 2018, Munich, Germany
  • Double angle theorems, 6th Croatian MathematicalCongress, June 14-17, 2016, Zagreb, Croatia
  • Relative Perturbation Theory for Definite Matrix Pairs, Joint Annual Meeting of GAMM and DMV, March 07-11, Braunschweig,  Germany
  • Relative Perturbation Theory for Definite Matrix Pairs and Hyperbolic Quadratic Eigenvalue Problem, Workshop on Matrix Equations and Tensor Techniques, September 21-22, Bologna, Italy
  • Eigensubspace perturbation theory for definite matrix pairs, Workshop within DAAD project Optimal Damping of Vibrating Systems, Osijek, October 7-10, 2014, Croatia.
  • The Rotation of Eigenspace of Perturbed Matrix Pairs, 5th Croation Mathematical Congress, Rijeka, June 18-21, 2012

 

Seminars and talks

  • Seminar za optimizaciju i primjene (Odjel za matematiku, Osijek), Geometrijski medijan u ravnini, 2009.
  • Seminar za Numeričku matematiku i računarstvo (PMF-Matematički odjel, Zagreb), Problem svojstvenih vrijednosti hermitskih matrica s "time reversal" simetrijom, 2012.
  • Topološki seminar, (PMF-Matematički odjel, Zagreb), A-beskonačno-prostori, A-beskonačno-algebre, A-beskonačno-operadi, 2012.
  • Seminar za Numeričku matematiku i računarstvo (PMF-Matematički odjel, Zagreb), Rotacija svojstvenih potprostora perturbiranih matričnih parova, 2013.
  • Seminar za optimizaciju i primjene (Odjel za matematiku, Osijek), Relativne perturbacijske ocjene ovisne o parametru i hiperbolički svojstveni problem,, 2014.
  • Seminar za optimizaciju i primjene (Odjel za matematiku, Osijek), Rotacija svojstvenog potprostora perturbiranih definitnih matričnih parova, 2014.
  • CSC Seminar (Max Planck Institute, Magdeburg), The Rotation of Eigenspace of Perturbed Matrix Pairs, 2015.

Participation in summer schools and workshops:

  • The third International School on Model Reduction for Dynamical Control Systems, 5 - 10 October 2015, Dubrovnik, Croatia
  • DAAD International School on Linear Optimal Control of Dynamic Systems, 23 - 28 September 2013, Osijek, Croatia
  • Summer School on Numerical Linear Algebra for Dynamical and High-Dimensional Problems, October 10-15, 2011, Trogir, Croatia
  • DAAD International School “Methods of Numerical Optimization “, May, 2012, Novi Sad/Serbia
  • DAAD International School “Hyperbolic Geometry and Arithmetics (Applications of the Selberg Trace Formula)”, October 3-10, 2010, Sarajevo/Bosnia

 

Study Visits Abroad

  • 14.02.-28.2.2015., 23.11.-28.11.2015. Max-Planck-Institut für Dynamik komplexer technischer Systeme, Magdeburg

Teaching

Teme završnih i diplomskih radova:

1.

 

Zimski semestar

Vektorski i unitarni prostori

Primijenjena i Inženjerska matematika - PTFOS

Matematika 1 - PTFOS

 

 

 Konzultacije (Office Hours):