Related papers: A naive procedure for computing angular spheroidal…
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…
This manuscript presents a novel and reliable third-order iterative procedure for computing the zeros of solutions to second-order ordinary differential equations. By approximating the solution of the related Riccati differential equation…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
Functionals with values in Non-Archimedean field of Laurent series applied to the definition of generalized solution (in the form of soliton and shock wave) of the Hopf equation and equations of elasticity theory. Calculation method for the…
In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds.…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
We study a variant of Newton's algorithm applied to under-determined systems of non-smooth equations. The notion of regularity employed in our work is based on Newton differentiability, which generalizes semi-smoothness. The classic notion…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
We develop some properties and the Bonnet formula for Clifford Gegenbauer polynomials. Then after we define and construct weighted Clifford prolate spheroidal wave functions. We then prove that they are orthogonal in a weighted function…
Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…
This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…
Semi-analytical methods for the modeling of guided waves in structures of constant cross-section lead to frequency-dependent polynomial eigenvalue problems for the wavenumbers and mode shapes. Solving these eigenvalue problems for a range…
Spin-weighted spheroidal harmonics are useful in a variety of physical situations, including light scattering, nuclear modeling, signal processing, electromagnetic wave propagation, black hole perturbation theory in four and higher…
Solving for the bound state eigenvalues of the Schr\"odinger equation is a tedious iterative process when the conventional shooting or matching method is used. In this work, we bypass the eigenvalue's dependence on the eigenfunction by…
We present a new computational approach for a class of large-scale nonlinear eigenvalue problems (NEPs) that are nonlinear in the eigenvalue. The contribution of this paper is two-fold. We derive a new iterative algorithm for NEPs, the…
We present a new adaptive circuit simulation algorithm based on spline wavelets. The unknown voltages and currents are expanded into a wavelet representation, which is determined as solution of nonlinear equations derived from the circuit…
A zero-finding technique for solving nonlinear equations more efficiently than they usually are with traditional iterative methods in which the order of convergence is improved is presented. The key idea in deriving this procedure is to…