Search results for "Newton's method"
showing 10 items of 16 documents
A generalized Newton iteration for computing the solution of the inverse Henderson problem
2020
We develop a generalized Newton scheme IHNC for the construction of effective pair potentials for systems of interacting point-like particles.The construction is made in such a way that the distribution of the particles matches a given radial distribution function. The IHNC iteration uses the hypernetted-chain integral equation for an approximate evaluation of the inverse of the Jacobian of the forward operator. In contrast to the full Newton method realized in the Inverse Monte Carlo (IMC) scheme, the IHNC algorithm requires only a single molecular dynamics computation of the radial distribution function per iteration step, and no further expensive cross-correlations. Numerical experiments…
A regularized Newton method for locating thin tubular conductivity inhomogeneities
2011
We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…
A New Procedure for the Evaluation of Non-Uniform Residual Stresses by the Hole Drilling Method Based on the Newton-Raphson Technique
2010
The hole drilling method is one of the most used semi-destructive techniques for the analysis of residual stresses in mechanical components. The non-uniform stresses are evaluated by solving an integral equation in which the strains relieved by drilling a hole are introduced. In this paper a new calculation procedure, based on the Newton-Raphson method for the determination of zeroes of functions, is presented. This technique allows the user to introduce complex and effective forms of stress functions for the solution of the problem. All the relationships needed for the evaluation of the stresses are obtained in explicit form, eliminating the need to use additional mathematical tools. The t…
�ber ein Verfahren der Ordnung $$1 + \sqrt 2 $$ zur Nullstellenbestimmung
1979
A new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions. The method needs as many function evaluations per step as the classical Newton method.
Some supplementary results on the 1+ $$\sqrt 2 $$ order method for the solution of nonlinear equations
1982
Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
Numerical study of the Kerr solution in rotating coordinates
2016
International audience; The Kerr solution in coordinates corotating with the horizon is studied as a testbed for a spacetime with a helical Killing vector in the Ernst picture. The solution is numerically constructed by solving the Ernst equation with a spectral method and a Newton iteration. We discuss convergence of the iteration for several initial iterates and different values of the Kerr parameters.
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
1999
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [ A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint,…
Some improvements in solving radial distributions networks through the backward/forward method
2005
In the electrical radial distribution networks analysis, the backward/forward method shows good features in terms of robustness, independence from load nature, small use of hardware resources and limited calculation time. In the present paper, some procedures to improve the b/f method with the aim of reducing the calculation time are presented. The adopted procedures regard the choice of the initial values of the nodes voltages and the way in which the convergence criterion is applied. The results of some tests carried out on some electrical test systems here reported have shown the efficiency of the proposed methodology in terms of calculation time reduction, especially when solving heavil…
The convergence of the perturbed Newton method and its application for ill-conditioned problems
2011
Abstract Iterative methods, such as Newton’s, behave poorly when solving ill-conditioned problems: they become slow (first order), and decrease their accuracy. In this paper we analyze deeply and widely the convergence of a modified Newton method, which we call perturbed Newton, in order to overcome the usual disadvantages Newton’s one presents. The basic point of this method is the dependence of a parameter affording a degree of freedom that introduces regularization. Choices for that parameter are proposed. The theoretical analysis will be illustrated through examples.
Parallel translations, Newton flows and Q-Wiener processes on the Wasserstein space
2022
- We extend the definition of Lott’s Levi-Civita connection to the Wasserstein space of probability measures having density and divergence. We give an extension of a vector field defined along an absolutely curve onto the whole space so that parallel translations can be introduced as done in differential geometry. In the case of torus, we prove the well-posedness of Lott’s equation for parallel translations.- We prove the well-posedness of the Newton flow equation on the Wasserstein space and show the connections between the relaxed Newton flow equation and the Keller-Segel equation.- We establish an intrinsic formalism for Itô stochastic calculus on the Wasserstein space throughout three k…