Inexact Newton methods for finding a zero of F 1 1 are variations of Newton's method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local linear model of F. Here, inexact Newton methods are formulated that incorporate features designed to improve convergence from arbitrary starting points. For each method, a basic global convergence ...

PURPOSE An emerging topic in diffusion magnetic resonance is imaging blood microcirculation alongside water diffusion using the intravoxel incoherent motion (IVIM) model. Recently, a combined IVIM diffusion tensor imaging (IVIM-DTI) model was proposed, which accounts for both anisotropic pseudo-diffusion due to blood microcirculation and anisotropic diffusion due to tissue microstructures. In t...

Each master iteration of a simpliied Newton algorithm for solving a system of equations starts by computing the Jacobian matrix and then uses this matrix in the computation of p Newton steps: the rst of these steps is exact, and the other are called \simpliied". In this paper we apply this approach to a large step path following algorithm for monotone linear complementarity problems. The result...

The Newton method and its variations are the most efficient methods known for solving systems of nonlinear equations when they are continuously differentiable. Besides its practical applications, the Newton method is also a powerful theoretical tool. One of the famous results on the Newton method is the well-known Kantorovich’s theorem, which has the advantage that the Newton sequence converges...

The use of Model Predictive Control is steadily increasing in industry as more complicated problems can be addressed. Due to that online optimization is usually performed, the main bottleneck with Model Predictive Control is the relatively high computational complexity. Hence, much research has been performed to find efficient algorithms that solve the optimization problem. As parallel hardware...

Peer two-step methods have been successfully applied to initial value problems for stiff and non-stiff ordinary differential equations both on parallel and sequential computers. Their essential property is the use of several stages per time step with the same accuracy. As a new application area these methods are now used for parameter-dependent ODEs where the peer stages approximate the solutio...

This paper proposes an implementable proximal quasi-Newton method for minimizing a nondifferentiable convex function f in <n . The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point p(xk) of xk to define a vk ∈ ∂ k f(p(xk))with k ≤ α‖vk‖,where α is a constant. The method monitors the reduction in the value ...

This paper is an attempt to address the processing of nonlinear numerical constraints over the Reals by combining three different methods: local consistency techniques, symbolic rewriting and interval methods. To formalize this combination, we define a generic two-step constraint processing technique based on an extension of the Constraint Satisfaction Problem, called Extended Constraint Satisf...

In this paper we propose a Modiied Block Newton Method for approximating an invariant subspace S and the corresponding eigenvalues of a symmetric matrix A. The method generates a sequence of matrices Z (k) which span subspaces S k approximating S. The matrices Z (k) are calculated via a Newton step applied to a special formulation of the block eigenvalue problem for the matrix A, followed by a ...

We explain an interface for the implementation of rate-independent elastoplasticity which separates the pointwise evaluation of the elastoplastic material law and the global solution of the momentum balance equation. The elastoplastic problem is discretized in time by diagonally implicit Runge-Kutta methods and every time step is solved with a Newton iteration. For the discretization in space t...