Related papers: On uncertainty quantification of eigenvalues and e…

In this article we are interested for the numerical computation of spectra of non-self adjoint quadratic operators, in two and three spatial dimensions. Indeed, in the multidimensional case very few results are known on the location of the…

Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…

We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…

Kinetic equations play a major rule in modeling large systems of interacting particles. Uncertainties may be due to various reasons, like lack of knowledge on the microscopic interaction details or incomplete informations at the boundaries.…

In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…

Eigenvalue problems for linear differential equations, such as time-independent Schr\"odinger equations, can be generalized to eigenvalue problems for nonlinear differential equations. In the nonlinear context a separatrix plays the role of…

We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such…

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…

We present an analysis of multilevel Monte Carlo techniques for the forward problem of uncertainty quantification for the radiative transport equation, when the coefficients ({\em cross-sections}) are heterogenous random fields. To do this,…

We consider conditions under which an embedded eigenvalue of a self-adjoint operator remains embedded under small perturbations. In the case of a simple eigenvalue embedded in continuous spectrum of multiplicity m < \infty we show that in…

We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…

We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…

The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators…

The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue problems. Using examples, we show that discretization can:…

Fast and accurate predictions of uncertainties in the computed dose are crucial for the determination of robust treatment plans in radiation therapy. This requires the solution of particle transport problems with uncertain parameters or…

In this paper, we investigate the eigenvalue problem for a non-local dispersal operator defined on a bounded spatial domain with Neumann-type boundary conditions. Unlike the classical Laplacian, the non-local operator lacks compactness,…

Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…

We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through…

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non…