A cubic regularization of Newton’s method with finite difference Hessian approximations

2021 ◽  
Author(s):  
G. N. Grapiglia ◽  
M. L. N. Gonçalves ◽  
G. N. Silva
Keyword(s):  
Finite Difference ◽  
Newton’S Method ◽  
Newton's Method ◽  
Cubic Regularization

Cascadic Newton’s method for the elliptic Monge–Ampère equation

2020 ◽  
Vol 18 (03) ◽  
pp. 2050018
Author(s):  
Qin Li ◽  
Zhiyong Liu
Keyword(s):  
Finite Difference ◽  
Newton’S Method ◽  
Newton's Method ◽  
Finite Difference Methods ◽  
Computation Time ◽  
Type Interpolation ◽  
Local Type ◽  
Cascadic Multigrid ◽  
Monge Ampere ◽  
Prolongation Operator

In this paper, a cascadic Newton’s method is designed to solve the Monge–Ampère equation. In the process of implementing the cascadic multigrid, we use the Full-Local type interpolation as prolongation operator and Newton iteration as smoother. In order to obtain Full-Local type interpolation, we provide several finite difference stencils. Especially, the skewed finite difference methods are first applied by us for the elliptic Monge–Ampère equation. Based on Full-Local interpolation techniques and cascade principle, the new algorithm can save a large amount of computation time. Some numerical experiments are provided to confirm the efficiency of our proposed method.

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

Sign in / Sign up

Export Citation Format

Share Document