Ivana Kuzmanović 

profilna

Assistant Professor

Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸

phone: +385-31-224-816
fax: +385-31-224-801
email:  ikuzmano @ mathos.hr
office:  3 (first floor)

 


Research Interests

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

Degrees

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

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

 


Publications

 
Journal Publications

  1. M. Essert, I. Kuzmanović, 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 https://www.schoolofhaskell.com/user/ivazler/linguistic.
  2. I. Kuzmanović, 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.
  3. I. Kuzmanović, 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.
  4. I. Kuzmanović, 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.
  5. I. Kuzmanović, 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, 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, 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, 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, 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


Others

  1. I. Kuzmanović, P. Corn, Razni načini zadavanja ravnine u prostoru , Osječki matematički list 12/1 (2012), 21-28
    Ravnina u prostoru može se jednoznačno odrediti pomoću normale na nju i jedne točke koja joj pripada. U ovom članku bit će pokazano jednoznačno zadavanje ravnine pomoću točaka i vektora u njoj, što se u konačnici može svesti na zadavanje točkom i normalom.
  2. I. Kuzmanović, Najbolja $l_infty$ aproksimacija rješenja sustava linearnih jednadžbi s jednom nepoznanicom, Osječki matematički list 11/1 (2011), 19-28
    U radu se promatra karakterizacija i metode određivanja najbolje $l_infty$ aproksimacije rješenja sustava linearnih jednadžbi s jednom nepoznanicom.
  3. I. Kuzmanović, Neke primjene funkcija pod i strop, Osječki matematički list 8/2 (2008), 77-82
    U radu su navedena neka svojstva funkcija pod i strop, te je ilustrirana njihova primjena.
  4. I. Kuzmanović, Udaljenost točke do krivulje, Osječki matematički list 5/2 (2005), 85-90
    U ovom članku razmatra se metoda računanja udaljenosti točke do eksplicitno, parametarski, te polarno zadane krivulje. U literaturi za ovaj problem postoji eksplicitno rješenje za slučaj afine funkcije, te za još neke specijalne slučajeve.


Books

  1. K. Burazin, J. Jankov, I. Kuzmanović, I. Soldo, Primjene diferencijalnog i integralnog računa funkcija jedne varijable, Sveučilište Josipa Jurja Strossmayera u Osijeku - Odjel za matematiku, Osijek, 2017.
  2. I. Kuzmanović, K. Sabo, Linearno programiranje, Sveučilište Josipa Jurja Strossmayera u Osijeku - Odjel za matematiku, Osijek, 2016.



Projects

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)

 


 

Workshop and Conference Talks

  • I.Kuzmanović, Parameter Dependent Generalized Sylvester and T-Sylvester Equations,  6th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2017), August 15-18, 2017, Budapest, Hungary.
  • I.Kuzmanović, Parameter dependent generalized Sylvester and T-Sylvester equations, METT VII — 7th Workshop on Matrix Equations and Tensor Techniques, 13-14 February 2017, Pisa, Italy
  • Ivana Kuzmanović, Optimization of the solution of Sylvester and $T$-Sylvester equations with applications, 16th GAMM ANLA Workshop, September 15-16, 2016, Hamburg, Germany

  • Ivana Kuzmanović, Damping optimization over the arbitrary time of the excited mechanical systems, 6th Croatian MathematicalCongress, June 14-17, 2016, Zagreb, Croatia

  • Ivana Kuzmanović, Structured Sylvester and T-Sylvester equations, 10th International Workshop on
    Accurate Solution of Eigenvalue Problems (IWASEP 10), Dubrovnik, June 2-5, 2014

  • I. Kuzmanović, Applications of Lyapunov and $T$-Lyapunov equations in mechanics, Fourth Mathematical Conference of the Republic of Srpska, Trebinje, 2014

  •  I. Kuzmanović, N.Truhar. Sherman-Morrison-Woodbury formula for Sylvester and T-Sylvester equation, 5th Croatian Mathematical Congress, June 18 - 21, 2012, Rijeka, Croatia

  •  Scitovski, Rudolf; Sabo, Kristian; Kuzmanović, Ivana; Vazler, Ivan; Cupec, Robert; Grbić, Ratko. The best least absolute deviation hyperplane - properties and efficient methods , 4th Croatian Mathematical Congress, Osijek, June 17-20, 2008

  •  I. Kuzmanović, The least absolute deviation linear regression: properties and two efficient methods, Aplimat, Bratislava, 2008

  •  I. Kuzmanović, R. Scitovski, Jedna metoda procjene parametara u smislu minimizacije sume $L_p$ ortogonalnih udaljenosti, PrimMath[2003], Zagreb

Seminars and talks

  • I. Kuzmanović, Structured Sylvester and $T$-Sylvester equations, Mathematical Colloquium, Osijek, 16.1.2014
  • I. Kuzmanović, Optimization of the solution of the parameter-dependent Sylvester equation, Optimization and Applications Seminar, Osijek, 29.6.2011.
  • I. Kuzmanović, Parameter-dependent Sylvester equation and applications, Optimization and Applications Seminar, Osijek, 8.6.2011.
  • I. Kuzmanović, Subgradient methods for minimization of nondifferentiable convex functions, Optimization and Applications Seminar, Osijek, 17.03.2010.
  • I. Kuzmanović, \textit{Functions floor and ceiling}, Winter math school, Osijek 2008.
  • I. Kuzmanović, Normal block matrices, Seminar for numerical mathematics, Zagreb, 13.3.2008.
  • I. Kuzmanović, Locations of lines in normed spaces, Optimization and Applications Seminar, Osijek, 07.3.2008.
  • I. Kuzmanović, Linear $l_\infty$ approximation, Optimization and Applications Seminar, Osijek, 09.1.2008.
  • I. Kuzmanović, Cantor normal form, Seminar for Logic and Foundations of Mathematics , Zagreb, 22.5.2007.

 

Participation in summer schools and workshops:

  • Workshop on Model Reduction Methods and Optimization, 20-21 September 2016, Opatija, Croatia
  • 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 Summer School on Sparse Eigenvalue Problems, August 22-27, 2011, Sarajevo, Bosnia and Herzegovina

Study Visits Abroad

  • 27.11.-3.12.2016. Max-Planck-Institut für Dynamik komplexer technischer Systeme, Magdeburg

 

Organization of International Meetings:

  • 2008. 4th Croatian Mathematical Congress - Organizing Committee Member

Refereeing/Reviewing

  •  International Journal of Systems Science
  •  International Journal of Computer Mathematics

Professional Societiey Membership

  • EMS (European Mathematical Society)
  • MAA (Mathematical Association of America)

 

 


Teaching

 

 

Obranjeni diplomski i završni radovi:

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

2. Jasna Okopni, Pozitivno definitne matrice, završni rad u komentorstvu s dr.sc. 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 dr.sc. Marijom Miloložom Pandur, 29.9.2017.

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

 

Teme diplomskih i završnih radova u akademskoj godini 2016./17.:

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

ZAVRŠNI RADOVI

  1. "Poluprosti operatori" (Ivana Crnković)
  2. "Kroneckerov produkt i operator vektorizacije" (pregled svojstava, ilustracija primjene) ( Karla Mercvajler)
  3. "Posteri u Latex-u" (Lucija Tatarević)
  4. "Dualni prostori" (Doris Aleksov)
  5. "Schurova dekompozicija matrice" (Matea Bolta)

DIPLOMSKI RADOVI

  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)

 

Konzultacije (Office Hours): 


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