Asisstant Professor

Ivana Kuzmanović Ivičić
3 (1st floor)
School of Applied Mathematics and Informatics

Josip Juraj Strossmayer University of Osijek

Research Interests

  • Applied mathematics
  • Numerical linear algebra
  • Matrix equations
  • Parameter dependent problems
  • Perturbation theory


PhD in Mathematics, Department of Mathematics, University of Zagreb, 2012.

BSc in Mathematics and Computer Science, Department of Mathematics, University of Osijek, Croatia, 2005.


Journal Publications

  1. I. Kuzmanović Ivičić, S. Miodragović, Perturbation bounds for stable gyroscopic systems in motion about an unstable equilibrium position, Journal of Computational and Applied Mathematics, (2024), prihvaćen za objavljivanje
    Relative perturbation bounds for stable linear gyroscopic systems $\displaystyle M \ddot x(t) + G\dot x(t) + K x(t) = 0$ are considered, where $M, K\in\mathbb{R}^{n\times n}$ are symmetric, $M$ is positive definite, $K$ negative definite and $G \in\mathbb{R}^{n\times n}$ is skew-symmetric such that $|G| > k M - k^{-1} K$ for some $k>0$. This means that all of the eigenvalues of the system are \textcolor{red}{purely} imaginary and semi-simple. For this kind of systems, we present an upper bound for the relative change in eigenvalues as well as the $\sin\Theta$ type bound for the corresponding eigenvectors under the perturbation of the system matrices. The performance of obtained bounds is illustrated in numerical experiments.
  2. S. Miodragović, N. Truhar, I. Kuzmanović Ivičić, Relative perturbation $\tan \Theta$ theorems for definite matrix pairs, Electronic Transactions on Numerical Analysis 60 (2024), 364-380
  3. I. Kuzmanović Ivičić, S. Miodragović, Perturbation bounds for stable gyroscopic systems, BIT Numerical Mathematics 63/1 (2023), 1-16
    In this paper we consider linear gyroscopic mechanical systems. More precisely, we consider the perturbation theory for stable gyroscopic systems. We present new relative perturbation bounds for the eigenvalues as well as the bounds for the perturbation of the corresponding eigenspaces. Derived bounds are dependent only on system matrices of the original and perturbed systems. The quality of obtained results is illustrated in the numerical experiment.
  4. I. Kuzmanović Ivičić, S. Miodragović, M. Ugrica, The tan Θ theorem for definite matrix pairs, Linear and multilinear algebra 70 (2022), 1-17
    In this paper, we consider the perturbation of a Hermitian matrix pair $(H,M)$, where $H$ and $M$ are non-singular and positive definite Hermitian matrices, respectively. A novel upper bound on a tangent of the angles between the eigenspaces of perturbed and unperturbed pairs is derived under a perturbation to the off-diagonal blocks of $H$. The rotation of the eigenspaces under a perturbation is measured in the matrix-dependent scalar product. We show that a $tanTheta$ bound for the standard eigenvalue problem is a special case of our new bound and that the obtained bound can be much sharper than the existing $sinTheta$ bounds.
  5. M. Essert, I. Kuzmanović Ivičić, I. Vazler, T. Žilić, Theory of M-system, Logic Journal of the IGPL 25/5 (2017), 836-858
    This paper introduces a new formal theory, the theory of M-system, which represents a many-valued logic system. Basic terms and concepts are defined which are the foundation for their further application. Though the theory comes from the field of electric circuitry, an attempt will be made to extend it to applications in linguistics. To check the examples used in this paper, a Haskell program was made, which can be found at
  6. I. Kuzmanović Ivičić, Z. Tomljanović, N. Truhar, Damping optimization over the arbitrary time of the excited mechanical system, Journal of Computational and Applied Mathematics, 304 (2016), 120-129
    In this paper we consider damping optimization in mechanical system excited by an external force. We use optimization criteria based on minimizing average energy amplitude and average displacement amplitude over the arbitrary time. As the main result we derive explicit formulas for objective functions. These formulas can be implemented efficiently and accelerate optimization process significantly, which is illustrated in a numerical example.
  7. I. Kuzmanović Ivičić, N. Truhar, Optimization of the solution of the parameter-dependent Sylvester equation and applications, Journal of Computational and Applied Mathematics, 237/1 (2013), 136-144
    This paper deals with an efficient algorithm for optimization of the solution of the parameter-dependent Sylvester equation $(A_0-vC_1C_2^T)X(v)+X(v)(B_0-vD_1D_2^T)=E, $ where $A_0$ is $mtimes m$, $B_0$ is $ntimes n$, $C_1$ and $C_2$ are $mtimes r_1$, $D_1$ and $D_2$ are $ntimes r_2$ and $X$ and $E$ are $mtimes n$ matrices. For optimization we use the following two optimization criteria: $tr(X(v))rightarrowmin$ and $|X(v)|_Frightarrowmin$. We present an efficient algorithm which derives formulas for the trace and for the Frobenius norm of the solution $X$ as functions $vrightarrowtr(X(v))$ and $vrightarrow|X(v)|_F$ as well as derivatives of these functions in a small amount of operations. That ensures fast optimization of these functions via standard optimization methods like the Newton method. A special case of this problem is a very important problem of dampers’ viscosity optimization in mechanical systems.
  8. I. Kuzmanović Ivičić, N. Truhar, Sherman-Morrison-Woodbury formula for Sylvester and $T$-Sylvester equation with applications, International Journal of Computer Mathematics 90/2 (2013), 306-324
    In this paper we present the Sherman-Morrison-Woodbury-type formula for the solution of the Sylvester equation of the form [(A_0+U_1V_1)X+X(B_0+U_2V_2)=E, ] as well as for the solution of the $T$-Sylvester equation of the form [ (A_0+U_1V_1)X+X^T(B_0+U_2V_2)=E, ] where $U_1, U_2, V_1, V_2$ are low-rank matrices. Although the matrix version of this formula for the Sylvester equation has been used in several different applications (but not for the case of a $T$-Sylvester equation), we present a novel approach using a proper operator representation. This novel approach allows us to derive a matrix version of the Sherman-Morrison-Woodbury-type formula for the Sylvester equation, as well as for the $T$-Sylvester equation which seems to be new. We also present algorithms for the efficient calculation of the solution of Sylvester and $T$-Sylvester equations by using these formulas and illustrate their application in several examples.
  9. I. Kuzmanović Ivičić, Z. Tomljanović, N. Truhar, Optimization of material with modal damping, Applied mathematics and computation 218 (2012), 7326-7338
    This paper considers optimal parameters for modal damping $D=Mf_1(M^{-1}K;alpha_1,dots,alpha_k)+Kf_2(K^{-1}M;alpha_1,dots,alpha_k)$ in mechanical systems described by the equation $Mddot{x}+Ddot{x}+Kx=0 $, where matrices $M$ and $K$ are mass and stiffness matrices, respectively. Different models of proportional and generalized proportional damping are considered and optimal parameters with respect to different optimization criteria related to the solution of the corresponding Lyapunov equation are given. Also, some specific example problems are compared with respect to the optimal and estimated parameters.

Refereed Proceedings

  1. I. Kuzmanović Ivičić, Z. Tomljanović, N. Truhar, Applications of Lyapunov and T-Lyapunov equations in mechanics, Fourth Mathematical Conference of the Republic of Srpska,, Trebinje, 2014, 83-92
    This paper considers Lyapunov and T -Lyapunov matrix equations. Lyapunov equation is a matrix equation of the form AX + XA^T = E which plays a vital role in a number of applications, while T -Lyapunov equation is a matrix equation of the form AX +X^TA^T = E. In this paper the relation between these equations will be exploit with purpose of applying obtained results in problems regarding damping optimization in mechanical systems.
  2. I. Kuzmanović Ivičić, G. Kušec, K. Sabo, R. Scitovski, A new method for searching an L_1 solution of an overdetermined system of linear equations and applications, 12th International Conference on Operational Research, Pula, Croatia, 2008, 309-319
  3. I. Kuzmanović Ivičić, R. Scitovski, K. Sabo, I. Vazler, The least absolute deviation linear regression: properties and two efficient methods, Aplimat 2008, Bratislava, 2008, 227-240
  4. R. Scitovski, I. Kuzmanović Ivičić, Jedna metoda procjene parametara u smislu minimizacije sume L_p ortogonalnih udaljenosti, Programski sustav Mathematica u znanosti, tehnologiji i obrazovanju. PrimMath[2003]. , Zagreb, Hrvatska, 2003, 147-157


  1. M. Andrijević, I. Kuzmanović Ivičić, Matematički model problema školskog rasporeda, Osječki matematički list 22 (2022), 119-129
    Problem školskog rasporeda vrlo je zastupljen problem koji s vremenom postaje sve složeniji jer je pri izradi rasporeda sve više uvjeta i ograničenja koji moraju biti zadovoljeni. U ovom radu prikazan je matematički model osnovnog problema rasporeda sati. Već u tom sasvim jednostavnom slučaju vidljivo je da se radi o vrlo složenom problemu koji svakim dodatnim uvjetom postaje sve složeniji sa sve manjim brojem rješenja. Danas je dostupno mnogo aplikacija koje pomažu pri izradi rasporeda, a sve se baziraju na nekoj matematičkoj metodi za pronalaženje optimalnog rješenja.
  2. D. Brajković Zorić, I. Kuzmanović Ivičić, M. Ribičić Penava, Matematičko natjecanje MathOS cup, Osječki matematički list 22/1 (2022), 81-89
    Cilj ovoga rada je predstaviti timsko natjecanje MathOS cup te dati pregled odabranih zadataka s rješenjima iz drugog kruga natjecanja MathOS cup 2022.


01.01.2020.–31.12.2023.  investigator on scientific project   Vibration Reduction in Mechanical Systems  (IP-2019-04-6774, VIMS). This project is fully supported by Croatian Science Foundation.

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

2007- 2013 investigator on  scientific project (235-2352818-1034)  “Nonlinear parameter estimation problems in mathematical models“ (Ministry of Science, Education and Sports)

Professional Activities

Udruga matematičara Osijek, vice president 2021.-2025.




Računalno razmišljanje i programiranje 1

Računalno razmišljanje i programiranje 2

Matematički alati

Linearna optimizacija

Matematika 1, Odjel za kemiju

Konzultacije (Office Hours): ponedjeljkom (Monday) u 10.

Obranjeni diplomski i završni radovi: (past  thesis)

1. Marija Mecanović, Metoda sukcesivne nadrelaksacije  (SOR), diplomski rad u komentorstvu s Zoranom Tomljanovićem, 15.9.2017.

2. Jasna Okopni, Pozitivno definitne matrice, završni rad u komentorstvu s Marijom Miloložom Pandur, 20.9.2017.

3. Nikolina Stupjak, Prezentacije u Latex-u, završni rad, 29.9.2017.

4.  Marinela Pilj, Generalizirani svojstveni problem i definitni matrični parovi, završni rad u komentorstvu s Marijom Miloložom Pandur, 29.9.2017.

5. Marija Mecanović, Iterativne metode za rješavanje linearnih sustava, završni rad, 29.9.2017.

6. Lucija Tatarević, Posteri u Latex-u, završni rad, 28.9.2018.

7. Doris Aleksov, Dualni prostori, završni rad, 28.9.2018.

8. Ana Mrkojević, Schurova dekompozicija matrice, završni rad, 30.9.2019.

9. Ivana Vuletić, Algebarska, analitička i geometrijska svojstva vektorskih normi, završni rad, 30.9.2019.

10. Maja Kovačević, Sylvesterova i Ljapunovljeva matrična jednadžba, završni rad, 29.9.2020.

11. Lea Mađarić, Geršgorinovi krugovi, završni rad, 23.10.2020.

12. Tonka Antić, Kreiranje grafičkih elemenata u LaTeX-u koristeći paket TikZ, završni rad, 15.09.2021.

13. Dunja Majdenić, Spektar i pseudospektar matrice, završni rad, 06.10.2021.


Teme diplomskih i završnih radova u akademskoj godini 2022./23. (available thesis topics):

Sljedeće teme su slobodne za diplomske i završne radove. Mole se zainteresirani studenti da se jave radi detaljnijih informacija.


  1. Vizualizacija u geometriji uz pomoć programskog paketa Mathematica
  2.  Animacije u programskom paketu Mathematica
  3. Primjena GeoGebre u nastavi matematike
  4. Krylovljevi potprostori i primjene
  5. Linearna algebra u genetici
  6. Kanonski oblik krivulje drugoga reda (Marko Jedlička)
  7. Kriterij konvergencije redova realnih brojeva (Marija Šeremet)



  1. “Matrične jednadžbe” (pregled osnovnih oblika jednadžbi kod kojih je nepoznanica matrica, pregled standardnih metoda za njihovo rješavanje, implementacija osnovnih metoda u Matlabu)
  2. “Generalizirane svojstvene vrijednosti”   (osnovne definicije i svojstva generaliziranih svojstvenih vrijednosti, QZ metoda za računanje generaliziranih svojstvenih vrijednosti, implementacija u Matlabu)
  3. “Tenzori”  (definicija i osnovni pojmovi vezani za tenzore (generalizirane matrice), pregled svojstava)
  4. Odabrani problemi linearne optimizacije (Tena Pavlić)
  5. Linearna algebra u strojnom učenju
  6. Ekipna matematička natjecanja u Hrvatskoj i u svijetu


Konzultacije (Office Hours): ponedjeljkom u 9h