Related papers: Structured backward errors for eigenvalues of line…
Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and…
We derive computable formulas for the structured backward errors of a complex number $\lambda$ when considered as an approximate eigenvalue of rational matrix polynomials that carry a symmetry structure. We consider symmetric,…
First, we derive explicit computable expressions of structured backward errors of approximate eigenelements of structured matrix polynomials including symmetric, skew-symmetric, Hermitian, skew-Hermitian, even and odd polynomials. We also…
We derive computable expressions of structured backward errors of approximate eigenelements of *-palindromic and *-anti-palindromic matrix polynomials. We also characterize minimal structured perturbations such that approximate…
We present a gradient-based calibration algorithm to identify a port-Hamiltonian system from given time-domain input-output data. The gradient is computed with the help of sensitivities and the algorithm is tailored such that the structure…
The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…
The modeling framework of port-Hamiltonian systems is systematically extended to constrained dynamical systems (descriptor systems, differential-algebraic equations). A new algebraically and geometrically defined system structure is…
In Parts I and II of this series of papers, three new methods for the computation of eigenvalues of singular pencils were developed: rank-completing perturbations, rank-projections, and augmentation. It was observed that a straightforward…
This paper presents an algorithm for checking and enforcing passivity of behavioral reduced-order macromodels of LTI systems, whose frequency-domain (scattering) responses depend on external parameters. Such models, which are typically…
A wide class of matrix pencils connected with dissipative Hamiltonian descriptor systems is investigated. In particular, the following properties are shown: all eigenvalues are in the closed left half plane, the nonzero finite eigenvalues…
In this paper, we compute the structured eigenvalue backward error of a Rosenbrock system matrix $S(z)=\left[\begin{array}{cc} A-zI & B \\ C & P(z) \end{array}\right]$ for a given scalar $\lambda\in \mathbb C$. We have developed simplified…
This paper presents a fast, randomized divide-and-conquer algorithm for the definite generalized eigenvalue problem, which corresponds to pencils $(A,B)$ in which $A$ and $B$ are Hermitian and the Crawford number $\gamma(A,B) =…
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…
This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in…
A generalized eigenvalue algorithm for tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some…
This paper is devoted to the study of perturbations of a matrix pencil, structured or unstructured, such that a perturbed pencil will reproduce a given deflating pair while maintaining the invariance of the complementary deflating pair. If…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
We present a gradient-based identification algorithm to identify the system matrices of a linear port-Hamiltonian system from given input-output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal…
Hermitian linear matrix pencils are ubiquitous in control theory, operator systems, semidefinite optimization, and real algebraic geometry. This survey reviews the fundamental features of the matricial solution set of a linear matrix…
Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…