Naslov
Optimization of the solution of the parameter-dependent Sylvester equation and applications

Autori
Kuzmanović, Ivana ; Truhar, Ninoslav

Izvornik
Journal of computational and applied mathematics (0377-0427) 237 (2013), 1; 136-144

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Parameter-dependent Sylvester equation; Optimization of the solution; Optimization of dampers' viscosity; Minimal trace; Minimal Frobenius norm

Sažetak
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 $m\times m$, $B_0$ is $n\times n$, $C_1$ and $C_2$ are $m\times r_1$, $D_1$ and $D_2$ are $n\times r_2$ and $X$ and $E$ are $m\times n$ matrices. For optimization we use the following two optimization criteria: $\tr(X(v))\rightarrow\min$ and $\|X(v)\|_F\rightarrow\min$. We present an efficient algorithm which derives formulas for the trace and for the Frobenius norm of the solution $X$ as functions $v\rightarrow\tr(X(v))$ and $v\rightarrow\|X(v)\|_F$ 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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