Related papers: Coupled anharmonic oscillators: the Rayleigh-Ritz …
We have developed a simple method to solve anharmonic oscillators equations. The idea of our method is mainly based on the partitioning of the potential curve into (n+1) small intervals, solving the Schr\"odinger equation in each…
The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…
Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without…
The new class of alternating-conjugate splitting methods is presented and analyzed. They are obtained by concatenating a given composition involving complex coefficients with the same composition but with the complex conjugate coefficients.…
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations…
Classical oscillators of sextic and octic anharmonicities are solved analytically up to the linear power of \lambda (Anharmonic Constant) by using Taylor series method. These solutions exhibit the presence of secular terms which are summed…
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schr\"{o}dinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller's original thawed Gaussian approximation, it…
Starting with an initial random network of oscillators with a heterogeneous frequency distribution, its autonomous synchronization ability can be largely improved by appropriately rewiring the links between the elements. Ensembles of…
The Rayleigh conjecture on the representation of the scattered field in the exterior of an obstacle $D$ is widely used in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture…
The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra. Conventional algorithms for its computation typically rely on matrix-adjoint products, making them sensitive to errors arising from…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective, where the information on the oscillatory coefficients in the…
We propose an alternative method to factorize an integer by using three harmonic oscillators. These oscillators are coupled together via specific Kerr nonlinear interactions. This method can be applied even if two harmonic oscillators are…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
This work is focused on the extension and assessment of the monotonicity-preserving scheme in [3] and the local bounds preserving scheme in [5] to hierarchical octree adaptive mesh refinement (AMR). Whereas the former can readily be used on…
This paper derives new inexact variants of the Douglas-Rachford splitting method for maximal monotone operators and the alternating direction method of multipliers (ADMM) for convex optimization. The analysis is based on a new inexact…
This paper is based on MacColl's [1] solution of the equation of motion for a linear (harmonic) oscillator subject to the laws of special relativity in the rest frame of the center of attraction. MacColl's result can be extended to the…
Purpose: To propose an alternating learning approach to learn the sampling pattern (SP) and the parameters of variational networks (VN) in accelerated parallel magnetic resonance imaging (MRI). Methods: The approach alternates between…
The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning (RL), and often an efficient approach to solving (or approximating the solution to) complex optimal control…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…