In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

We present an implicit immersed boundary method for the incompressible Navier–Stokes equations capable of handling three-dimensional membrane–fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton–Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free appr...

A nonmonotone strategy for solving nonlinear systems of equations is introduced. The idea consists of combining eecient local methods with an algorithm that reduces monotonically the squared norm of the system in a proper way. The local methods used are Newton's method and two quasi-Newton algorithms. Global iterations are based on recently introduced box-constrained minimization algorithms. We...

In this work we introduce a technique for solving nonlinear systems that improves the order of convergence of any given iterative method which uses the Newton iteration as a predictor. The main idea is to compose a given iterative method of order pwith a modification of the Newton method that introduces just one evaluation of the function, obtaining a new method of order p + 2. By applying this...

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. The Euler equations are discretized on each block independently using second-order accurate summation-by-parts operators and scalar numerical dissipation. Boundary conditions are imposed and block interfaces are coupled using simultaneous approximation terms (SATs). ...

This paper describes a method for fitting 3D object model to still (single) 2D observed image by searching for the model's optimum posture parameters in the parameter space through LMM iteration method (a stabilized Gauss-Newton method). In the method, we propose a new approach to feeding an excellent initial parameter value to the iteration method via aspect identification by applying linear c...

This paper focuses on the generation of dynamic models for an articulated forestry machine. Such models can be used for training simulators, for sizing components, and for control. The most complex model includes base compliance, and pendulum-like motions of the processing head suspended from an end-point. A Newton-Euler iterative method, implemented symbolically, is used to include base degree...

The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...

In this paper we provide implementable methods for solving nondifferentiable convex optimization problems. A typical method minimizes an approximate Moreau–Yosida regularization using a quasi-Newton technique with inexact function and gradient values which are generated by a finite inner bundle algorithm. For a BFGS bundle-type method global and superlinear convergence results for the outer ite...