Newton Methods for Nonlinear Problems

By Peter Deuflhard. 2004

657 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0b95810694baf36687cd5ccdc044a56758aed1fc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

Citations in the corpus

Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results (2011, methodology): “Their approach, directly evolved from techniques for convex problems and elaborating on [9], makes use of the cubic model mG k (s) with Gk = σk G, where G is positive definite and σk is an estimate of the global Lipschitz constant (the techniques for updating σk are similar to Griewank’s).”
Analysis of fracture in thin shells by overlapping paired elements (2006, methodology): “The solution method is the residual-based damped Newton method (see also [29]) with arc-length continuation method.”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, methodology): “, x be roots of p identified with some iterative algorithm, such as Newton’s method [20].”
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation (2017, methodology): “On the other hand, if Qk+1 ≥ 1, the new residual is larger than the old one and we have the situation in which a monotonicity-based Newton method would fail and, for example, an error-oriented version may perform better [22].”
Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation (2009, background): “An excellent overview of the field is given in [13].”
An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact (2016, methodology): “An alternate to the Newton-Raphson method are quasi-Newton methods such as the secant and Broyden methods, which do not require the evaluation of the Jacobian at each iteration step; however, they are linear and superlinearly convergent in the neighborhood of the actual solution, respectively [30, 3”
Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions (2008, methodology): “We propose to determine the root(s) τ of F by Newton’s method (see [14, 4] for instance).”
Adaptive Space-Time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems (2007, methodology): “The well known motivation (see for instance Deuflhard [26]) of the classical ordinary Newton method for solving a nonlinear operator equation”