Related papers: The Eigenvalue Problem for Linear and Affine Itera…
Let $\left( X,\left\Vert \cdot\right\Vert_{X}\right) $ and $\left( Y,\left\Vert \cdot\right\Vert_{Y}\right) $ be Banach spaces over $\mathbb{R},$ with $X$ uniformly convex and compactly embedded into $Y.$ The inverse iteration method is…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
In this paper, we give a numerical analysis for the transmission eigenvalue problem by the finite element method. A type of multilevel correction method is proposed to solve the transmission eigenvalue problem. The multilevel correction…
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…
We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…
The nonlinear eigen-problem $ Ax+F(x)=\lambda x$ is studied where $A$ is an $n\times n$ irreducible Stieltjes matrix. Under certain conditions, this problem has a unique positive solution. We show that, starting from a multiple of the…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…
Consider $n$ linearly independent vectors in $\mathbb{C}^n$ which form columns of a matrix $A$. The recursive evaluation of eigen directions (normalized eigenvectors) of $A$ is the solution of an eigenvalue problem of the form…
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…
In this work, we study discontinuous Sturm-Liouville type problems with eigenparameter dependent boundary condition and transmission conditions at three interior points. A self-adjoint linear operator A is defined in a suitable Hilbert…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
This paper provides results for eigencurves associated with self-adjoint linear elliptic boundary value problems. The elliptic problems are treated as a general two-parameter eigenproblem for a triple (a, b, m) of continuous symmetric…
The problem of computing recurrence coefficients of sequences of rational functions orthogonal with respect to a discrete inner product is formulated as an inverse eigenvalue problem for a pencil of Hessenberg matrices. Two procedures are…
The Orr-Sommerfeld equation with linear profile on the finite interval is considered. The behavior of the spectrum of this problem is completely investigated for large Reynolds numbers. The limit curves are found to which the eigenvalues…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider $\dot x_\alpha(t) = (G + \alpha(t) F)x_\alpha(t)$, where $G$ and…
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this…
We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…