A structure-preserving doubling algorithm for quadratic eigenvalue problems arising from time-delay systems

AbstractWe propose a structure-preserving doubling algorithm for a quadratic eigenvalue problem arising from the stability analysis of time-delay systems. We are particularly interested in the eigenvalues on the unit circle, which are difficult to estimate. The convergence and backward error of the algorithm are analyzed and three numerical examples are presented. Our experience shows that our algorithm is efficient in comparison to the few existing approaches for small to medium size problems

Model reduction by moment matching for linear singular systems

© 2015 IEEE.The paper presents a moment matching approach to the model reduction problem for singular systems. Combining the interpolation-based and the steady-state-based description of moment, a partitioned formulation of the Krylov projector is obtained. Several implications of this result are investigated and different families of reduced order models are proposed. The possibility to maintain structural properties of system is studied. Two examples illustrate the results of the paper

On the (non)existence of best low-rank approximations of generic IxJx2 arrays

Several conjectures and partial proofs have been formulated on the (non)existence of a best low-rank approximation of real-valued IxJx2 arrays. We analyze this problem using the Generalized Schur Decomposition and prove (non)existence of a best rank-R approximation for generic IxJx2 arrays, for all values of I,J,R. Moreover, for cases where a best rank-R approximation exists on a set of positive volume only, we provide easy-to-check necessary and sufficient conditions for the existence of a best rank-R approximation

The intersection problems of parametric curve and surfaces by means of matrix based implicit representations

In this paper, we introduce and study a new implicit representation of parametric curves and parametric surfaces . We show how these representations which we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of geometric modeling and Computer Aided Geometric Design (CAGD) : The curve/curve, urve/surface and surface/surface intersection problems, the point-on-curve and inversion problems, the computation of singularities points