相关论文: Computing the first eigenpair for problems with va…

We report the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. In these refinements we used an observation by Booth that has made…

We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain.…

The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Bj\"{o}rck and Pereyra algorithm for solving…

In this short note, the simplicity of the first eigenvalue of a nonlinear system is shown by an alternative proof; thereby, it states that the first eigenfunctions are unique up to modulo scaling.

We find upper and lower bounds for the first eigenvalue and the volume entropy of a noncompact real analytic K\"ahler manifold, in terms of Calabi's diastasis function and diastatic entropy, which are sharp in the case of the complex…

We deal with $m$-component vector-valued solutions to the Cauchy problem for linear both homogeneous and nonhomogeneous weakly coupled second order parabolic system in the layer ${\mathbb R}^{n+1}_T={\mathbb R}^n\times (0, T)$. We assume…

This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…

This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…

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…

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…

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…

This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to…

We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the…

The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…

We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…

This work is devoted to the study of the first order operator $x'(t)+m\,x(-t)$ coupled with periodic boundary value conditions. We describe the eigenvalues of the operator and obtain the expression of its related Green's function in the non…

We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville-Gel'fand problem associated to solutions which blow-up at m points. Our problem is the case with an…

We consider the eigenvalue problem for the magnetic Schr\"odinger operator and take advantage of a property called gauge invariance to transform the given problem into an equivalent problem that is more amenable to numerical approximation.…

Many Engineering Problems could be mathematically described by Final Value Problem, which is the inverse problem of Initial Value Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the…

Prime factorization is an outstanding problem in arithmetic, with important consequences in a variety of fields, most notably cryptography. Here we employ the intriguing analogy between prime factorization and optical interferometry in…