Related papers: Approximation of PDE eigenvalue problems involving…
Consider the following optimization problem: Given $n \times n$ matrices $A$ and $\Lambda$, maximize $\langle A, U\Lambda U^*\rangle$ where $U$ varies over the unitary group $\mathrm{U}(n)$. This problem seeks to approximate $A$ by a matrix…
This paper is devoted to study the qualitative properties of hybrid measure differential equations (HMDEs, for short). We establish several results on the existence of global solutions, including the existence of regulated, continuous,…
We study the existence and localization of eigenvalue-eigenfunction pairs for parameter-dependent Neumann BVPs with a functional term. By reformulating the problems as a Hammerstein integral equation, we apply an existence and localization…
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
When studying boundary value problems for some partial differential equations arising in applied mathematics, we often have to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find…
For linear Hamiltonian $2n\times 2n$ systems $J y'(x) = (\lambda W(x)+H(x))y(x)$ we investigate the problem how the eigenvalues $\lambda$ depend on the entries of the coefficient matrix $H$. This question turns into a deformation equation…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
Asymptotics of the eigenvalues can always be derived for self-adjoint boundary value problems. However, they can also be derived for boundary value problems that fail to be self-adjoint provided that they are Birkhoff regular. A regular…
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 derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
When a system of first order linear ordinary differential equations has eigenvalues of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The cost of representing…
The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or…
This paper studies the numerical approximation of evolution equations by nonlinear parametrizations $u(t)=\Phi(\param(t))$ with time-dependent parameters $\param(t)$, which are to be determined in the computation. The motivation comes from…
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…
The dependence on the domain is studied for the Dirichlet eigenvalues of an elliptic operator considered in bounded domains. Their proximity is measured by a norm of the difference of two orthogonal projectors corresponding to the reference…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
We investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation (PLDE). Two kinds of polynomials are to be distinguished, we call them /periodic/ and…