the computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. it is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of new-ton's method, but previous researchers have mentioned that some...

In this note we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. We show how known theory for the noise-free case can be extended and thereby provide a partial explanation for the good performance of quasi...

A fast Newton–Krylov algorithm is presented that solves the turbulent Navier–Stokes equations on unstructured 2-D grids. Themodel of Spalart andAllmaras provides the turbulent viscosity and is loosely coupled to themean-flow equations. It is often assumed that the turbulence model must be fully coupled to obtain the full benefit of an inexact Newton algorithm. We demonstrate that a loosely coup...

A Newton method to solve total least squares problems for Toeplitz systems of equations is considered. When coupled with a bisection scheme, which is based on an eecient algorithm for factoring Toeplitz matrices, global convergence can be guaranteed. Circulant and approximate factorization preconditioners are proposed to speed convergence when a conjugate gradient method is used to solve linear...

A Newton method to solve total least squares problems for Toeplitz systems of equations is considered. When coupled with a bisection scheme, which is based on an eecient algorithm for factoring Toeplitz matrices, global convergence can be guaranteed. Circulant and approximate factorization preconditioners are proposed to speed convergence when a conjugate gradient method is used to solve linear...

An efficient black-box algorithm for self-consistent analysis of three-dimensional (3-D) microelectromechanical systems (MEMS) is described. The algorithm is matrix-free based and employs a multilevel Newton technique to solve the coupled electromechanical equations. The new approach is shown to converge very rapidly and is much faster than relaxation algorithm for tightly coupled cases. While ...

In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that...

This work presents recent progress in phase-field-based fracture modeling in heterogeneous porous media. Existing algorithms that have been developed in the last years are extended to tackle three-dimensional configurations. Our solution technique is formulated in terms of a nested Newton loop that combines a primal-dual active set method (required for treating the crack irreversibility) and a ...