Ninoslav Truhar (Google Scholar Profile)
Full Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests

 Numerical Linear Algebra
 Systems and Control Theory
 Applied Mathematics
Degrees

 B. S. in Mathematics and Physics 1987, University of Osijek
 M. S. In Mathematics 1995, University of Zagreb
 Ph.D. in Mathematics 2000, University of Zagreb
Study Visits Abroad and Professional Improvement
 1997 1012, visiting researher at The Pennsylvania State University, State College, PA, USA
 1999–2001 postPh. D. research at FernUniversitat in Hagen, Germany
 2003 guest professor at FernUniversitat in Hagen, Germany (one month)
 2004 guest professor at FernUniversitat in Hagen, Germany (one month)
 2006 visiting researher at Department of Mathematics, University of Kentucky,
Lexington, Kentucky, USA  2007 visiting professor at Department of Mathematics at the University of Texas
at Arlington, Arlington, Texas, USA (one semester)  2013 visiting professor at Department of Mathematics at the University of Texas
at Arlington, Arlington, Texas, USA (one semester)
Publications
 N. Truhar, R. Li, On an EigenvectorDependent Nonlinear Eigenvalue Problem from the Perspective of Relative Perturbation Theory, Journal of Computational and Applied Mathematics, 395 (2021)We are concerned with the eigenvectordependent nonlinear eigenvalue problem (NEPv) $H(V)V = V Lambda$, where $H(V) in bbC^{n times n}$ is a Hermitian matrixvalued function of $V in bbC^{n times k}$ with orthonormal columns, i.e., $V^{HH} V = I_k$, $k leq n$ (usually $k ll n$). Sufficient conditions on the solvability and solution uniqueness of NEPv are obtained, based on the wellknown results from the relative perturbation theory. These results are complementary to recent ones in [Cai, Zhang, Bai, and Li, {em SIAM J. Matrix Anal. Appl.}, 39:2 (2018), pp.13601382], where, among others, one can find conditions for the solvability and solution uniqueness of NEPv, based on the wellknown results from the absolute perturbation theory. Although the absolute perturbation theory is more versatile in applications, there are cases where the relative perturbation theory produces better results.
 P. Benner, X. Liang, S. Miodragović, N. Truhar, Relative Perturbation Theory for Quadratic Hermitian Eigenvalue Problem, Linear algebra and its applications 618 (2021), 97128In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $(lambda^2 M + lambda C + K)x = 0$, where $M$ and $K$ are nonsingular Hermitian matrices and $C$ is a general Hermitian matrix. These results are based on new relative perturbation bounds for an equivalent regular Hermitian matrix pair $Alambda B$. The new bounds can be applied to quadratic eigenvalue problems appearing in many relevant applications, such as mechanical models with indefinite damping. The quality of our bounds is demonstrated by several numerical experiments.
 N. Truhar, Z. Tomljanović, R. Li, Perturbation Theory for Hermitian Quadratic Eigenvalue Problem  Damped and Simultaneously Diagonalizable Systems, Applied mathematics and computation 371 (2020)The main contribution of this paper is a novel approach to the perturbation theory of a structured Hermitian quadratic eigenvalue problems $(lambda^2 M + lambda D + K) x=0$. We propose a new concept without linearization, considering two structures: general quadratic eigenvalue problems (QEP) and simultaneously diagonalizable quadratic eigenvalue problems (SDQEP). Our first two results are upper bounds for the difference $left  X_2^* M widetilde{;X};_1 _F^2   X_2^* M {;X};_1 _F^2 right$, and for $ X_2^* M widetilde X_1  X_2^* M X_1_F$, where the columns of $X_1=[x_1, ldots, x_k]$ and $X_2=[x_{;k+1};, ldots, x_n]$ are linearly independent right eigenvectors and $M$ is positive definite Hermitian matrix. As an application of these results we present an eigenvalue perturbation bound for SDQEP. The third result is a lower and an upper bound for $sin{;Theta(mathcal{;X};_1, widetilde{;mathcal{;X};};_1)}; _F$, where $Theta$ is a matrix of canonical angles between the eigensubspaces $mathcal{;X};_1 $ and $widetilde{;mathcal{;X};};_1$, $mathcal{;X};_1 $ is spanned by the set of linearly independent right eigenvectors of SDQEP and $widetilde{;mathcal{;X};};_1$ is spanned by the corresponding perturbed eigenvectors. The quality of the mentioned results have been illustrated by numerical examples.
 N. Truhar, A Note on an Upper and a Lower Bound on Sines between Eigenspaces for regular Hermitian Matrix Pairs, Journal of Computational and Applied Mathematics, 358 (2019), 374384The main results of the paper are un upper and a lower bound for the Frobenius norm of the matrix $sin Theta$, of the sines of the canonical angles between unperturbed and perturbed eigenspaces of a regular generalized Hermitian eigenvalue problem $A x = lambda B x$ where $A$ and $B$ are Hermitian $n times n$ matrices, under a feasible nonHermitian perturbation. As one application of the obtained bounds we present the corresponding upper and the lower bounds for eigenspaces of a matrix pair $(A,B)$ obtained by a linearization of regular quadratic eigenvalue problem $left( lambda^2 M + lambda D + K right) u = 0 $, where $M$ is positive definite and $D$ and $K$ are semidefinite. We also apply obtained upper and lower bounds to the important problem which considers the influence of adding a damping on mechanical systems. The new results show that for certain additional damping the upper bound can be too pessimistic, but the lower bound can reflect a behaviour of considered eigenspaces properly. The obtained results have been illustrated with several numerical examples.
 N. Truhar, Z. Tomljanović, M. Puvača, Approximation of damped quadratic eigenvalue problem by dimension reduction, Applied mathematics and computation 347 (2019), 4053This paper presents an approach to the efficient calculation of all or just one important part of the eigenvalues of the parameter dependent quadratic eigenvalue problem $(lambda^2(mathbf{;v};) M + lambda(mathbf{;v};) D(mathbf{;v};) + K) x(mathbf{;v};) = 0$, where $M, K$ are positive definite Hermitian $ntimes n$ matrices and $D(mathbf{;v};)$ is an $ntimes n$ Hermitian semidefinite matrix which depends on a damping parameter vector $mathbf{;v};= begin{;bmatrix}; v_1 & ldots & v_k end{;bmatrix};in mathbb{;R};_+^k$. With the new approach one can efficiently (and accurately enough) calculate all (or just part of the) eigenvalues even for the case when the parameters $v_i$, which in this paper represent damping viscosities, are of the modest magnitude. Moreover, we derive two types of approximations with corresponding error bounds. The quality of error bounds as well as the performance of the achieved eigenvalue tracking are illustrated in several numerical experiments.
Projects

Principal Investigator: Optimization of parameter dependent mechanical systems (IP2014099540; OptPDMechSys). This project has been fully supported by Croatian Science Foundation for the period 01.07.2015.30.06.2019.
 Mixed Integer Nonlinear Programming (MINLP) for damper optimizationscientific project; supported by the DAAD for period 20152016 (Project director); partner institution: Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg

European Model Reduction Network (EUMORNET). Funded by: COST (European Cooperation in Science and Technology).
Partner: researchers in model order reduction from 17 countries.
 DAAD: Optimal Damping of Vibrating Systems, PPP Germany, 20132015
Project run 01/01/2013  12/31/2014 founded by DAAD in collaboration between Max Planck Institute for Dynamics Complex Technical Systems Magdeburg, Computational Methods in Systems and Control Theory, Magdeburg, Germany and Department of Mathematics, University of Osijek, Osijek, Croatia

Solution of largescale Lyapunov Differential Equations,
Funded by: FWF Austrian Science Fundation, FWF project id: P27926
Researchers: Dr. Hermann Mena (project director, University of Innsbruck, Innsbruck, Austria); Prof. Dr. Alexander Ostermann (University of Innsbruck, Innsbruck, Austria)
Partners: Universidad Jaime I, Castellon (Spain), University of Tuebingen, (Germany),
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg (Germany), Department of Mathematics, University of Osijek (Croatia)
Editorial Service
Member of Editorial Board:
 Numerical Algebra, Control and Optimization (since 2021)
 Mathematics (MDPI) (since 2021)
 Mathematical Communications (since 2007)
 Osječki matematički list (since 2003)
Forthcoming Meetings
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 Workshop on Model Reduction Methods and Optimization, 2021 September 2016, in Opatija, Croatia, http://www.mathos.unios.hr/index.php/443.
 The third International School on Model Reduction for Dynamical Control Systems, 5  10 October 2015, in Dubrovnik, Croatia http://www.mathos.unios.hr/index.php/351
 Member of the Scientific Committee of the 6th Croatian Congress of Mathematics (Zagreb, 2016)
 Organizer of the DAAD International School on Linear Optimal Control of Dynamic Systems, 23  28 September 2013, Osijek http://www.mathos.unios.hr/locschool2013/

Member of the Scientific Committee of the 5th Croatian Congress of Mathematics (Rijeka, 2012) http://www.math.uniri.hr/CroMC2012/

Organizer of the Summer School on Numerical Linear Algebra for Dynamical and HighDimensional Problems, October 1015, 2011, Trogir, Croatia, http://www.mpimagdeburg.mpg.de/mpcsc/events/trogir/

Member of the Scientific Committee of the 4th Croatian Congress of Mathematics (Osijek, 2008) http://www.mathos.hr/congress2008/
Refereeing/Reviewing
Refereeing
 SIAM Journal on Matrix Analysis and Applications (SIMAX)
 SIAM Journal on Scientific Computing (SISC)
 Linear Algebra and its Applications (LAA)
 Numerische Mathematik
 BIT Numerical Mathematics
 Mathematical and Computer Modelling (MCM)
 Applied Mathematics and Computation (AMC)
 International Journal of Computer Mathematics
 Journal of Applied Mathematics and Computing (JACM)
 Journal of Sound and Vibration
 International Journal of Systems Science
 International Journal of Computer Mathematics
 Numerical Algorithms
 Central European Journal of Mathematics
 Bulletin of the Iranian Mathematical Society
 Glasnik matematički
 Mathematical Communications
Reviewing  AMS Mathematical Review (since 2006)
 Zentralblatt MATH
Service Activities

Chairman of Osijek Mathematical Society, 20032013

Chairman of the Mathematical Colloquium, 20052017
Teaching
Konzultacije (Office Hours): Utorak (Tue) 11:30am12:15pm, Srijeda (Wed) 11:30am12:15pm. Konzultacije su moguće i po dogovoru.
Diplomska nastava:
Teme za diplomske radove: popis tema
Novo:
Personal
 Birthdate: May 4, 1963
 Birthplace: Osijek, Croatia
 Citizenship: Croatian
 Family: Married
Hobbies:
I am a fan and supporter of basketball club KK Vrijednosnice Osijek
http://www.kkvrijednosniceosijek.hr/
https://hrhr.facebook.com/pages/KKVrijednosniceOsijek/117543455032023