Quasi-Newton and truncated-Newton methods are popular methods in optimization, and are traditionally seen as useful alternatives to the gradient and Newton methods. Throughout the literature, results are found that link quasi-Newton methods to certain first-order methods under various assumptions. We offer a simple proof to show that a range of quasi-Newton methods are first-order methods in th...

A b s t r a c t . A procedure for soìving nonìinear time-marching problems is presented. The nonsymmetric systems of equations arising from Newton-type linearizations are solved using an iterativestrategy based on the Generalized Minimal RESidual (GMRES) algorithm. Matrix-free techniques ìeading to reduction in Storage are presented. Incorporation of a linesearch algorithm in the Newton-GMRES s...

For the nonlinear analysis of structures using the well known Newton-Raphson Method, the tangent stiffness matrices of the elements must be constructed in each iteration. Due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the Newton-Raphson method to reduce the cost and time required by the analysis. In this paper, a ...

Restarting GMRES, a linear solver frequently used in numerical schemes, is known to suffer from stagnation. In this paper, a simple strategy is proposed to detect and avoid stagnation, without modifying the standard GMRES code. Numerical tests with the modified GMRES(m), GMRESH(m) procedure, alone and as part of an inexact Newton procedure with several choices for the forcing term, demonstrate ...

A fast and accurate method for Generalized Harmonic Analysis (GHA) is proposed. The proposed method estimates the parameters of a sinusoid and subtracts it from a target signal one by one. The frequency of the sinusoid is estimated around a peak of Fourier spectrum using Newton’s method, which is much faster than search methods. The amplitude and the phase are estimated to minimize the squared ...

We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized ele...

An efficient multi-block Newton–Krylov algorithm using the compressible Navier–Stokes equations is presented for the analysis and design of high-lift airfoil configurations. The preconditioned generalized minimum residual (GMRES) method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Furthermore, the GMRES method is used ...