Model order reduction (MOR) is common in simulation, control and optimization of complex dynamical systems arising in modeling of physical processes and in the spatial discretization of parabolic partial differential equations (PDEs) in two or more dimensions. Typically, after a semidiscretization of the differential operator by the finite element method (FEM) or by the boundary element method,...

The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylvester matrix of given lower rank. We present algorithms for computing the nearest GCD and a certified 2-GCD for...

The problem of approximating the greatest common divisor(GCD) for multivariate polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylvester matrix of given lower rank. We present algorithms for computing the nearest GCD and a certif...

An alternative simple proof for a well-known result encountered in blind identification and equalization of communication channels is derived. It is shown that the coprimeness condition of a number of FIR channels is equivalent to the full column rank condition of a certain block Sylvester matrix, whose entries are the channel coefficients. As a corollary, it is also shown that in general, the ...

Introduction E IGENSTRUCTURE assignment algorithms are widely used to design control systems.Most of the available eigenstructure assignment algorithms assign all of the eigenvalues to the desired values.The eigenstructureassignmentalgorithmcan be dividedinto two groups, that is, the null space approach and Sylvester equation approach.The null spaceapproachis used to solvemode decoupling proble...

Recent ScaLAPACK-style implementations of the BartelsStewart method and the iterative matrix-sign-function-based method for solving continuous-time Sylvester matrix equations are evaluated with respect to generality of use, execution time and accuracy of computed results. The test problems include well-conditioned as well as illconditioned Sylvester equations. A method is considered more genera...

In this paper, the eigenvalues of various non-Sylvester Hadamard matrices constructed by monomial permutation matrices are derived, which shows the relation between the eigenvalues of the newly constructed matrix and Sylvester Hadamard matrix. * The authors are with School of Electrical Engineering and Computer Science, Seoul National University, Seoul, Korea, ([email protected]). Paper No....