Related papers: New and efficient method for solving the eigenvalu…
This paper presents methodology for the computation of whole sets of heteroclinic connections between iso-energetic slices of center manifolds of center x center x saddle fixed points of autonomous Hamiltonian systems. It involves: (a)…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions' eigenvalue problem. Expanding the super-potential in series of the parameter alpha, the first order term of ground…
We propose a two-sided Lanczos method for the nonlinear eigenvalue problem (NEP). This two-sided approach provides approximations to both the right and left eigenvectors of the eigenvalues of interest. The method implicitly works with…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr\"odinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms:…
Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algorithms, establishing a relationship to system realization…
Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…
The discretized Bethe-Salpeter eigenvalue problem arises in the Green's function evaluation in many body physics and quantum chemistry. Discretization leads to a matrix eigenvalue problem for $H \in \mathbb{C}^{2n\times 2n}$ with a…
In this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions with nonconvex processes. By…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the…
We investigate two-field cosmological model with phantom and canonical fields (phantonical model as a generalisation of the quintom model for global universe evolution, including early inflationary stage). The model is represented as the…
The problem of diffraction of an electromagnetic plane wave by a perfectly conducting circular disk and its complementary problem, diffraction by a circular hole in an infinite conducting plate, are rigorously solved using the method of the…
In this paper, we present a new iterative approximate method of solving boundary value problems. The idea is to compute approximate polynomial solutions in the Bernstein form using least squares approximation combined with some properties…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. While there exists a large literature on the existence of solutions for special settings, there are only few numerical solution methods…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We derive a generalized zero-range pseudopotential applicable to all partial wave solutions to the Schroedinger equation based on a delta-shell potential in the limit that the shell radius approaches zero. This properly models all higher…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…