27th Conference of the International Linear Algebra Society (ILAS 2026)

Session

Matrix Nearness Problems

MS 05

May 18, 2026, 11:00 AM

78. Nearest matrix with multiple eigenvalues by Riemannian optimization

Vanni Noferini (Aalto University)

5/18/26, 11:00 AM

Matrix Nearness Problems

Minisymposium Talk

Given a square complex matrix $A$, we tackle the problem of finding the nearest matrix with multiple eigenvalues or, equivalently when $A$ had distinct eigenvalues, the nearest defective matrix. To this goal, we extend the general framework described in [M. Gnazzo, V. Noferini, L. Nyman, F. Poloni, Riemann-Oracle: A general-purpose Riemannian optimizer to solve nearness problems in matrix...

86. Robustly asymptotically stable dissipative Hamiltonian descriptor systems

Volker Mehrmann (TU Berlin)

5/18/26, 11:25 AM

Matrix Nearness Problems

Minisymposium Talk

We analyze the robust asymptotic stability under structure-preserving perturbations for the class of linear time-invariant dissipative-Hamiltonian differential-algebraic (dHDAE) systems. We show how to compute the distance to the nearest singular and high index system and determine stability radii for the finite spectrum under structure preserving perturbations

123. Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics

Simon Mataigne (UCLouvain)

5/18/26, 11:50 AM

Matrix Nearness Problems

Minisymposium Talk

We give bounds on geodesic distances on the Stiefel manifold, derived from new geometric insights. The considered geodesic distances are induced by the one-parameter family of Riemannian metrics introduced by Hüper et al. (2021), which contains the well-known Euclidean and canonical metrics. First, we give the best Lipschitz constants between the distances induced by any two members of the...

465. Reliably Computing the Worst-case H-infinity Norm of a Parametric System Using an Interpolation-based Algorithm.

Tim Mitchell (CUNY Queens College & The Graduate Center)

5/18/26, 2:00 PM

Matrix Nearness Problems

Minisymposium Talk

In this talk, we consider computing the worst-case (highest) $\mathcal{H}_\infty$ norm of a either a continuous-time or discrete-time linear time-invariant parametric system, where the state-space matrices all depend on a single real-valued scalar parameter $\mathsf{p}$ on a domain $\mathcal{P}$ consisting of a finite number of intervals. On each interval in $\mathcal{P}$, we assume that...

177. Distance to prescribed rank matrix polynomials via generic factorizations and alternating least squares

Froilán M. Dopico (Universidad Carlos III de Madrid (Spain))

5/18/26, 2:25 PM

Matrix Nearness Problems

Minisymposium Talk

We propose an algorithm that approximates a given matrix polynomial of any degree $d$ by another matrix polynomial of a prescribed rank and degree at most $d$. The algorithm combines recent advances in the theory of generic factorizations for matrix polynomials of bounded rank and degree with an alternating least squares strategy. For $d=1$, the algorithm includes the important case of matrix...

230. Structured stability radii of dissipative Hamiltonian systems

Anshul Prajapati (Max Planck Institute for Dynamics of Complex Technical Systems)

5/18/26, 2:50 PM

Matrix Nearness Problems

Minisymposium Talk

We study linear time-invariant Dissipative Hamiltonian (DH) systems arising in energy-based modeling of dynamical systems. An advantage of DH systems is that they are always stable due to the structure of their coefficient matrices, and, under further weak conditions, even asymptotically stable. Here, we consider the computation of the stability radii for a given asymptotically stable DH...

289. Constrained Rayleigh quotient optimization and its applications in polynomial eigenvalue problem

Punit Sharma (Indian Institute of Technology Delhi - Abu Dhabi, UAE)

5/19/26, 11:00 AM

Matrix Nearness Problems

Minisymposium Talk

Let $G, H_1,\ldots,H_s \in \mathbb C^{n,n}$ be Hermitian and $S_1,\ldots,S_k \in \mathbb C^{n,n}$ be symmetric matrices. In this talk, we maximize the Rayleigh quotient of a Hermitian matrix $H$ under certain constraints involving Hermitian matrices $H_1,\ldots, H_s$ and symmetric matrices $S_1,\ldots, S_k$. More specifically, we...

361. Singular Value Characterizations for a Nearest Rectangular Polynomial Matrix with an Eigenvalue

Emre Mengi (Koc University, Istanbul)

5/19/26, 11:25 AM

Matrix Nearness Problems

Minisymposium Talk

A rectangular polynomial matrix with more columns than rows generically has no eigenvalues. We aim to find a smallest perturbation (with respect to the 2-norm of the concatenated coefficients of the polynomial matrix) so that the perturbed polynomial matrix has an eigenvalue, that is prescribed. This problem is motivated by locating a nearest uncontrollable system for a first-order, as well as...

136. A Newton–bisection method with monotone convergence for matrix nearness problems.

Nicola Guglielmi (Gran Sasso Science Institute)

5/19/26, 11:50 AM

Matrix Nearness Problems

Minisymposium Talk

In this talk, I will address eigenvalue-optimization-based matrix nearness problems such as the stability radius of a matrix or a time invariant system, $\mathcal{H}^\infty$ norm computation, the structured distance to singularity.

These are formulated here as 2-variable optimization problems of functionals depending either on a single or on several target eigenvalues of the matrix.
It is...