Related papers: A reduced scalar potential approach for magnetosta…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Newton method is one of the most powerful methods for finding solutions of nonlinear equations and for proving their existence. In its "pure" form it has fast convergence near the solution, but small convergence domain. On the other hand…
The multiconfiguration self-consistent field (MCSCF) method is revisited with a specific focus on two-electron systems for simplicity. The wave function is represented as a linear combination of Slater determinants. Both the orbitals and…
This paper focuses on discussing Newton's method and its hybrid with machine learning for the steady state Navier-Stokes Darcy model discretized by mixed element methods. First, a Newton iterative method is introduced for solving the…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of this inverse source problem is conditionally logarithmic.…
The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field…
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…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
As an effective emulator of ill-conditioned power flow, continuous Newton methods (CNMs) have been extensively investigated using explicit and implicit numerical integration algorithms. Explicit CNMs are prone to non-convergence issues due…
The energy-based vector hysteresis model of Francois-Lavet et al. establishes an implicit relation between magnetic fields and fluxes via internal magnetic polarizations which are determined by convex but non-smooth minimization problems.…
The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
Factor Analysis is an effective way of dimensionality reduction achieved by revealing the low-rank plus sparse structure of the data covariance matrix. The corresponding model identification task is often formulated as an optimization…