The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...

A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method, which assumes perturbed Jacobians at each step. Its high convergence orders were characterized by Dennis and Moré [Math. Comp. 28 (1974), 549–560]. The inexact Newton method constitutes another such model, since it assumes that at each step the linear systems are only approximat...

A fundamental computational procedure in practically all areas of scientific computing is the calculation of the Newton step (in n-dimensions). In many cases this computation represents the dominant cost in the overall computing task. Typically the Newton step computation breaks down into two separable subtasks: calculation of the Jacobian (or Hessian) matrix along with the right-hand-side, and...

We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward ...

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based...

In this paper we present a Newton scoring algorithm for the maximum likelihood separation and direction of arrival estimation of constant modulus signals, using a calibrated array. The main technical step is the inversion of the Fisher information matrix, and an analytic formula for the update step in the Newton method. We present the algorithm based on the derived update and discuss potential ...

We propose a new algorithm for the non-negative ICA problem, based on the rotational nature of optimization over a set of square orthogonal (orthonormal) matrices W, i.e. where W W = WW = In. Using a truncated Fourier expansion of J(t), we obtain a Newton-like update step along the steepest-descent geodesic, which automatically approximates to a usual (Taylor expansion) Newton update step near ...

Naive implementations of Newton's method for unconstrained N-stage discrete-time optimal control problems with Bolza objective functions tend to increase in cost like N 3 as N increases. However, if the inherent recursive structure of the Bolza problem is properly exploited, the cost of computing a Newton step will increase only linearly with N. The efficient Newton implementation scheme propos...

The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...

We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. T...