Page 660 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 660
OPTIMIZATION AND CONTROL
Optimization of parameter dependent structured Sylvester and
T -Sylvester equations
Ivana Kuzmanovic´ Ivicˇic´, ikuzmano@mathos.hr
University of Osijek, Croatia
Sylvester and T -Sylvester equations are matrix equations of the form AX + XB = E and
AX + XT B = E, respectively, where A, B and E are given and X is unknown matrix.
Sylvester equations appear frequently in many areas of applied mathematics. For example,
Sylvester equations play vital roles in matrix eigen-decompositions, control theory, model re-
duction, numerical solution of matrix differential Riccati equations and algebraic Riccati equa-
tion, image processing, and many more. On the other hand, T -Sylvester matrix equations have
recently attracted attention of researchers because of their relationship with palindromic eigen-
value problems.
This talk will be focused on structured Sylvester and T - Sylvester equations, especially on
structured problems with system matrices of the form A = A0 + U1V1 and B = B0 + U2V2
where U1, U2, V1 and V2 are small rank update matrices. Sherman-Morrison-Woodbury-type
formula for the solutions of this type of equations will be given. The obtained formula is used
for the construction of an algorithm that solves the equations of the above form much more
efficiently than the standard algorithms.
Application of obtained algorithms will be illustrated on the damping optimization problem.
Hyperbolic quadratic eigenvalue problem and frequency isolation
Suzana Miodragovic´, ssusic@mathos.hr
University of Osijek, Croatia
Coauthors: Ninoslav Truhar, Julio Moro, Frenando de Teran
The solution of the forced system undergo large oscillations whenever some eigenvalue of the
corresponding quadratic eigenvalue problem
λ2M + λC + K x = 0, 0 = x ∈ Cn,
is close to the frequency of the external force. One way to avoid resonance is to modify matrices
M , C and K in such a way that the new system has no eigenvalues close to these frequencies.
This frequency isolation problem is considered for the hyperbolic QEP.
New shape derivative formula for solving a free boundary problem of
Bernoulli’s type
Azeddine Sadik, sadik.ufrnantes@gmail.com
Laboratory of Mathematics and Applications,
Faculty of Sciences and Technics Beni Mellal, Morocco
Coauthors: Abdesslam Boulkhemair, Abdelkrim Chakib
In this paper, we deal with a new numerical method for the approximation of a class of free
boundary problem reformulated as a shape optimizationone, which consist in minimizing an
appropriate cost functional. We startby showing the existence of the shape derivative of the
658
Optimization of parameter dependent structured Sylvester and
T -Sylvester equations
Ivana Kuzmanovic´ Ivicˇic´, ikuzmano@mathos.hr
University of Osijek, Croatia
Sylvester and T -Sylvester equations are matrix equations of the form AX + XB = E and
AX + XT B = E, respectively, where A, B and E are given and X is unknown matrix.
Sylvester equations appear frequently in many areas of applied mathematics. For example,
Sylvester equations play vital roles in matrix eigen-decompositions, control theory, model re-
duction, numerical solution of matrix differential Riccati equations and algebraic Riccati equa-
tion, image processing, and many more. On the other hand, T -Sylvester matrix equations have
recently attracted attention of researchers because of their relationship with palindromic eigen-
value problems.
This talk will be focused on structured Sylvester and T - Sylvester equations, especially on
structured problems with system matrices of the form A = A0 + U1V1 and B = B0 + U2V2
where U1, U2, V1 and V2 are small rank update matrices. Sherman-Morrison-Woodbury-type
formula for the solutions of this type of equations will be given. The obtained formula is used
for the construction of an algorithm that solves the equations of the above form much more
efficiently than the standard algorithms.
Application of obtained algorithms will be illustrated on the damping optimization problem.
Hyperbolic quadratic eigenvalue problem and frequency isolation
Suzana Miodragovic´, ssusic@mathos.hr
University of Osijek, Croatia
Coauthors: Ninoslav Truhar, Julio Moro, Frenando de Teran
The solution of the forced system undergo large oscillations whenever some eigenvalue of the
corresponding quadratic eigenvalue problem
λ2M + λC + K x = 0, 0 = x ∈ Cn,
is close to the frequency of the external force. One way to avoid resonance is to modify matrices
M , C and K in such a way that the new system has no eigenvalues close to these frequencies.
This frequency isolation problem is considered for the hyperbolic QEP.
New shape derivative formula for solving a free boundary problem of
Bernoulli’s type
Azeddine Sadik, sadik.ufrnantes@gmail.com
Laboratory of Mathematics and Applications,
Faculty of Sciences and Technics Beni Mellal, Morocco
Coauthors: Abdesslam Boulkhemair, Abdelkrim Chakib
In this paper, we deal with a new numerical method for the approximation of a class of free
boundary problem reformulated as a shape optimizationone, which consist in minimizing an
appropriate cost functional. We startby showing the existence of the shape derivative of the
658
