Adaptive tangential interpolation in rational Krylov subspaces for MIMO dynamical systems. (English) Zbl 1314.65085
The authors analysis the Krylov-type subspace method for a reduction of a linear dynamical system with many inputs and construct the tangential modification of this method. The method consists in the generation of the sequence of the interpolation poles \( s_{i}\) and tangential directions \( d_{i}\) by maximizing the residual norm. Also, this method is applied for the matrix \( A \) stemming from the discretization of the operator
\[
L(u) = ( e^{-xy}u_{x})_{x}+ ( -e^{xy}u_{y})_{y}
\]
and the comparison with other methods is shown. The content of the article is exposed in an unsuccessful manner.
Reviewer: Ivan Secrieru (Chişinău)
MSC:
65K10 | Numerical optimization and variational techniques |
93D25 | Input-output approaches in control theory |
93C05 | Linear systems in control theory |
65F10 | Iterative numerical methods for linear systems |