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We continue the work of [Camano, Lackner, Monk, SIAM J. Math. Anal., Vol. 49, No. 6, pp. 4376-4401 (2017)] on electromagnetic Stekloff eigenvalues. The authors recognized that in general the eigenvalues due not correspond to the spectrum of…
We study the eigenvalues and eigenfunctions of a differential operator that governs the asymptotic behavior of the unsupervised learning algorithm known as Locally Linear Embedding when a large data set is sampled from an interval or disc.…
Maximization and minimization problems of the principle eigenvalue for divergence form second order elliptic operators with the Dirichlet boundary condition are considered. The principal eigen map of such elliptic operators is introduced…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
Coordinate descent methods have considerable impact in global optimization because global (or, at least, almost global) minimization is affordable for low-dimensional problems. Coordinate descent methods with high-order regularized models…
How do the geometric properties of a domain impact the spectrum of an operator defined on it? How do we compute accurate and reliable approximations of these spectra? The former question is studied in spectral geometry, and the latter is a…
It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive…
This paper is concerned with the Dirichlet eigenvalue problem for Laplace operator in a bounded domain with periodic perforation in the case of small volume. We obtain the optimal quantitative error estimates independent of the spectral…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a…
One of the hard optimization problems that has a semi-definite relaxation with quantitative bound on the approximation error is the maximization of a convex quadratic form on the hypercube. The relaxation not only yields an upper bound on…
We study ill-conditioned positive definite matrices that are disturbed by the sum of $m$ rank-one matrices of a specific form. We provide estimates for the eigenvalues and eigenvectors. When the condition number of the initial matrix tends…
It is shown how mixed finite element methods for symmetric positive definite eigenvalue problems related to partial differential operators can provide guaranteed lower eigenvalue bounds. The method is based on a classical compatibility…
This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on $\ell_2$, the space of square summable…
In this paper we present a mathematical and numerical analysis of an eigenvalue problem associated to the elasticity-Stokes equations stated in two and three dimensions. Both problems are related through the Herrmann pressure. Employing the…
We compute the asymptotic for the eigenvalues of a particular class of compact operators deeply linked with the second variation of optimal control problems. We characterize this family in terms of a set of finite dimensional data and we…
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex…
The article is devoted to the development of numerical methods for solving variational inequalities with relatively strongly monotone operators. We consider two classes of variational inequalities related to some analogs of the Lipschitz…