Related papers: Eigenvalue Bounds for Double Saddle-Point Systems

In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…

The order parameter of a critical system defined in a layered parallel plate geometry subject to Neumann boundary conditions at the limiting surfaces is studied. We utilize a one-particle irreducible vertex parts framework in order to study…

In this work, we introduce two algorithmic frameworks, named Bregman extragradient method and Bregman extrapolation method, for solving saddle point problems. The proposed frameworks not only include the well-known extragradient and…

We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…

We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet-Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the…

This work is concerned with finite range bounds on the variance of individual eigenvalues of random covariance matrices, both in the bulk and at the edge of the spectrum. In a preceding paper, the author established analogous results for…

Observing renewed interest in long-standing (semi-) relativistic descriptions of bound states, we would like to make a few comments on the eigenvalue problem posed by the spinless Salpeter equation and, illustrated by the examples of the…

Let $(\Sigma^2,ds^2)$ be a compact Riemannian surface, possibly with boundary, and consider Schr\"odinger-type operators of the form $L=\Delta+V-aK$ together with natural Robin and Steklov-type boundary conditions incorporating a boundary…

Let $U\subset \mathbb{R}^n$ ($n\geq 3$) be an exterior Euclidean domain with smooth boundary $\partial U$. We consider the Steklov eigenvalue problem on $U$. First we derive a sharp lower bound for the first eigenvalue in terms of the…

In this paper, we extend to the block case, the a posteriori bound showing superlinear convergence of Conjugate Gradients developed in [J. Comput. Applied Math., 48 (1993), pp. 327-341]; that is, we obtain similar bounds, but now for block…

With the dual variational principle and the saddle point reduction we use the abstract bifurcation theory recently developed by author in previous work to prove many new bifurcation results for solutions of four types of Hamiltonian…

To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive…

We develop a unified nonparametric framework for sharp partial identification and inference on inequality indices when the data contain coarsened observations of the variable of interest. We characterize the extremal allocations for all…

We derive inequalities for sums of eigenvalues of Schr\"{o}dinger operators on finite intervals and tori. In the first of these cases, the inequalities converge to the classical trace formulae in the limit as the number of eigenvalues…

A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\"odinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here we show that in the…

Non-stationary approximations of the final value of a converging sequence are discussed, and we show that extremal eigenvalues can be reasonably estimated from the CG iterates without much computation at all. We introduce estimators of…

The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel--Darboux form constructed from sequences of biorthogonal polynomials. For…

We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}\Phi(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling…

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…

We propose confining dualities of $\mathcal{N}=(0,2)$ half-BPS boundary conditions in 3d $\mathcal{N}=2$ supersymmetric $SU(N)$, $USp(2n)$ and $SO(N)$ gauge theories. Some of these dualities have the novel feature that one (anti)fundamental…