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
 J. Moro, S. Miodragović, F. de Teran, N. Truhar, Frequency isolation for gyroscopic systems via hyperbolic quadratic eigenvalue problems, Mechanical Systems and Signal Processing 184/109688 (2023), 119The solutions of a forced gyroscopic system of ODEs may undergo large oscillations whenever some eigenvalues of the corresponding quadratic eigenvalue problem (QEP) $(lambda^2 M + lambda G+K)v=0,quad 0 neq v in mathbb{C}^n,$ are close to the frequency of the external force (both $M,K$ are symmetric, $M$ is positive definite, $K$ is definite and $G$ is skewsymmetric). This is the phenomenon of {colr the} socalled resonance. One way to avoid resonance is to modify some (or all) of the coefficient matrices, $M$, $G$, and $K in mathbb{R}^{ntimes n}$ in such a way that the new system has no eigenvalues close to these frequencies. This is known as the frequency isolation problem. In this paper we present frequency isolation algorithms for tridiagonal systems in which only the gyroscopic term $G$ is modified. To derive these algorithms, the real gyroscopic QEP is first transformed into a complex hyperbolic one, which allows to translate many of the ideas in textcolor{red}{[Mech. Syst. Signal Process., 75:1126, 2016]} for undamped systems into the full quadratic framework. Some numerical experiments are presented.
 N. Truhar, M. Petrač, Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix, Mathematics 10 (2022), 121We present two novel results for small damped oscillations described by the vector differential equation $M ddot{x} + C dot{x} + K x = 0$, where the mass matrix $M$ can be singular, but standard deflation techniques cannot be applied. The first result is a novel formula for the solution ${X}$ of the Lyapunov equation {${A}^T {X} + {X} {A} = I$,} where ${A}={A}(v)$ is obtained from $M, C(v) in mathbb{R}^{n times n}$, and $K in mathbb{R}^{n times n} $, which are the socalled mass, damping, and stiffness matrices, respectively, and $rank(M)=n1$. Here, $C(v)$ is positive semidefinite with $rank({C}(v))=1$. Using the obtained formula, we propose a very efficient way to compute the optimal damping matrix. The second result was obtained for a different structure, where we assume that $dim(mathcal{N}(M))geq 1$ and internal damping exists (usually a small percentage of the critical damping). For this structure, we introduce a novel linearization, i.e., a novel construction of the matrix $A$ in the Lyapunov equation {$A^T{X} + {X}{A} =  {I}$,} and a novel optimization process. The proposed optimization process computes the optimal damping $C(v)$ that minimizes a function $vmapsto{rm trace}({Z}{X})$ (where ${Z}$ is a chosen symmetric positive semidefinite matrix) using the approximation function $g(v) = c_v + frac{a}{v} + bv$, for the trace function $f(v) doteq {rm trace}({Z}{X}(v))$. Both results are illustrated with several corresponding numerical examples.
 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.
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:
 Computational Mathematics and Computer Modeling with Applications (since 2022)
 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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 11th Conference on Applied Mathematics and Scientific Computing 59 September 2022, Brijuni, Croatia
 10th Conference on Applied Mathematics and Scientific Computing 1418 September 2020, Brijuni, Croatia
 Ninth Conference on Applied Mathematics and Scientific Computing 1720 September 2018, Solaris, Šibenik, Croatia
 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