Related papers: Tolerances, robustness and parametrization of matr…
A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-off? errors, making it a formidable challenge in numerical computation particularly when the matrix is known through approximate data. This paper…
In this short paper, a matrix perturbation bound on the eigenvalues found by principal component analysis is investigated, for the case in which the data matrix on which principal component analysis is performed is a convex combination of…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
Standard optimality criteria (e.g. A-, D-optimality criterion, etc.) have been commonly used for obtaining optimal designs. For a given statistical model, standard criteria assume the error variance is known at the design stage. However, in…
A problem of paramount importance in both pure (Restricted Invertibility problem) and applied mathematics (Feature extraction) is the one of selecting a submatrix of a given matrix, such that this submatrix has its smallest singular value…
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
The spectra of signed matrices have played a fundamental role in social sciences, graph theory, and control theory. In this work, we investigate the computational problems of identifying symmetric signings of matrices with natural spectral…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining…
Model reparametrization, which follows the change-of-variable rule of calculus, is a popular way to improve the training of neural nets. But it can also be problematic since it can induce inconsistencies in, e.g., Hessian-based flatness…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
The exact parameter values of mathematical models are often uncertain or even unknown. Nevertheless, we may have access to crude information about the parameters, e.g., that some of them are nonzero. Such information can be captured by…
In this paper, we address the problem of computing the maximal admissible robust positive invariant (MARPI) set for discrete-time linear time-varying systems with parametric uncertainties and additive disturbances. The system state and…
Many practical optimization problems involve uncertain parameters that are strictly positive. However, the most common uncertainty sets used in robust optimization are the box and the ellipsoidal sets, which may include non-positive values…
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the performance of machine learning models. Deeply rooted in algebraic topology, persistent…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…