Related papers: Pseudosingularity in the eigenvalue integral equat…
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…
The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a constructive procedure for solving this problem, prove…
It is known that singular values of idempotent matrices are either zero or larger or equal to one \cite{HouC63}. We state exactly how many singular values greater than one, equal to one, and equal to zero there are. Moreover, we derive a…
This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the…
We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
Differential equations where the graph of some derivative of a function is composed of a finite number of similarity transformations of the graph of the function itself are defined. We call these self-similar differential equations (SSDEs)…
A new method for finding first integrals of discrete equations is presented. It can be used for discrete equations which do not possess a variational (Lagrangian or Hamiltonian) formulation. The method is based on a newly established…
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…
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 aim of the present work is to introduce a method based on Chebyshev polynomials for the numerical solution of a system of Cauchy type singular integral equations of the first kind on a finite segment. Moreover, an estimation error is…
The properties of the first (largest) eigenvalue and its eigenvector (first eigenvector) are investigated for large sparse random symmetric matrices that are characterized by bimodal degree distributions. In principle, one should be able to…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
Singular chain spaces for linear relations in linear spaces play a fundamental role in the decomposition of linear relations in finite-dimensional spaces. In this paper singular chains and singular chain spaces are discussed in detail for…
We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference (Miao et al. [2018], Tchetgen Tchetgen et al. [2020]). Proximal causal inference…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…