Related papers: Backward errors for multiple eigenpairs in structu…
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…
This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…
We consider numerical approximations of overdamped Langevin stochastic differential equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution…
In this paper, we give some lower bounds for several eigenvalues. Firstly, we investigate the eigenvalues $\lambda_i$ of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the eigenvalues to general…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…
The Matrix Decomposition techniques have been a vital computational approach to analyzing the hierarchy of functional connectivity in the human brain. However, there are still four shortcomings of these methodologies: 1). Large training…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
The relative distance between eigenvalues of the compression of a not necessarily semibounded self-adjoint operator to a closed subspace and some of the eigenvalues of the original operator in a gap of the essential spectrum is considered.…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
The worst situation in computing the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation associated with an M-matrix occurs when the corresponding linearizing matrix has two very small eigenvalues, one with positive…
In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…
This paper deals with the estimation of the distance between the solution of a static linear mechanic problem and its approximation by the finite element method solved with a non-overlapping domain decomposition method (FETI or BDD). We…
Let $G_n$ be an $n \times n$ matrix with real i.i.d. $N(0,1/n)$ entries, let $A$ be a real $n \times n$ matrix with $\Vert A \Vert \le 1$, and let $\gamma \in (0,1)$. We show that with probability $0.99$, $A + \gamma G_n$ has all of its…
The eigenfunctions and eigenvalues of the Fokker-Planck operator with linear drift and constant diffusion are required for expanding time-dependent solutions and for evaluating our recent perturbation expansion for probability densities…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…
This book is about solving matrix nearness problems that are related to eigenvalues or singular values or pseudospectra. These problems arise in great diversity in various fields, be they related to dynamics, as in questions of robust…
Prior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential ${\rm e}^{tA}v$, is extended to the case of associated $\varphi$-functions (which occur within the class…
A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the outliers of eigenvalues. In this work, we investigate the…