Some Reflections on the Continuous Newton-Method for Rational Functions

1980 ◽  
pp. 131-147 ◽  
Author(s):  
Hubertus Th. Jongen ◽  
Peter Jonker ◽  
Frank Twilt
Keyword(s):  
Newton Method ◽  
Rational Functions ◽  
Continuous Newton Method

On the Convergence Rate of the Continuous Newton Method

2019 ◽  
Vol 239 (6) ◽  
pp. 867-879
Author(s):  
A. Gibali ◽  
D. Shoikhet ◽  
N. Tarkhanov
Keyword(s):  
Convergence Rate ◽  
Newton Method ◽  
Continuous Newton Method

A perfect memory makes the continuous Newton method look ahead

2017 ◽  
Vol 92 (8) ◽  
pp. 085201
Author(s):  
M B Kim ◽  
J W Neuberger ◽  
W P Schleich
Keyword(s):  
Newton Method ◽  
Look Ahead ◽  
Continuous Newton Method ◽  
Perfect Memory

An extended continuous Newton method

1990 ◽  
Vol 67 (1) ◽  
pp. 57-77 ◽  
Author(s):  
I. Diener ◽  
R. Schaback
Keyword(s):  
Newton Method ◽  
Continuous Newton Method

CONTINUOUS NEWTON METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATION

2010 ◽  
Vol 24 (13) ◽  
pp. 1303-1306
Author(s):  
Q.-D. CAI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Newton Method ◽  
Jacobian Matrix ◽  
Algebraic Equations ◽  
Partial Differential ◽  
Linear Algebraic Equations ◽  
Non Linear ◽  
Non Linear System ◽  
Continuous Newton Method

Newton method is a widely used iteration method in solving nonlinear algebraic equations. In this method, a linear algebraic equations need to be solved in every step. The coefficient matrix of the algebraic equations is so-called Jacobian matrix, which needs to be determined at every step. For a complex non-linear system, usually no explicit form of Jacobian matrix can be found. Several methods are introduced to obtain an approximated matrix, which are classified as Jacobian-free method. The finite difference method is used to approximate the derivatives in Jacobian matrix, and a small parameter is needed in this process. Some problems may arise because of the interaction of this parameter and round-off errors. In the present work, we show that this kind of Newton method may encounter difficulties in solving non-linear partial differential equation (PDE) on fine mesh. To avoid this problem, the continuous Newton method is presented, which is a modification of classical Newton method for non-linear PDE.

scholarly journals Identification of Flexural Rigidity in a Kirchhoff Plates Model Using a Convex Objective and Continuous Newton Method

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
B. Jadamba ◽  
R. Kahler ◽  
A. A. Khan ◽  
F. Raciti ◽  
B. Winkler
Keyword(s):  
Inverse Problem ◽  
Newton Method ◽  
Fourth Order ◽  
Flexural Rigidity ◽  
Numerical Study ◽  
Variable Parameter ◽  
Kirchhoff Plates ◽  
Estimation Problems ◽  
Output Least Squares ◽  
Continuous Newton Method

This work provides a detailed theoretical and numerical study of the inverse problem of identifying flexural rigidity in Kirchhoff plate models. From a mathematical standpoint, this inverse problem requires estimating a variable coefficient in a fourth-order boundary value problem. This inverse problem and related estimation problems associated with general plates and shell models have been investigated by numerous researchers through an optimization framework using the output least-squares (OLSs) formulation. OLS yields a nonconvex framework and hence it is suitable for investigating only the local behavior of the solution. In this work, we propose a new convex framework for the inverse problem of identifying a variable parameter in a fourth-order inverse problem. Existence results, optimality conditions, and discretization issues are discussed in detail. The discrete inverse problem is solved by using a continuous Newton method. Numerical results show the feasibility of the proposed framework.

The continuous Newton method

1988 ◽  
Vol 5 (1) ◽  
pp. 327-329
Author(s):  
Harold E. Benzinger
Keyword(s):  
Newton Method ◽  
Continuous Newton Method

Strong singularities and the continuous Newton method

Equadiff 99 ◽  
2000 ◽  
pp. 925-927 ◽  
Author(s):  
Ricardo Riaza ◽  
Pedro J. Zufiria
Keyword(s):  
Newton Method ◽  
Continuous Newton Method

scholarly journals Finite-Time Stable Versions of the Continuous Newton Method and Applications to Neural Networks

2009 ◽  
Vol 42 (19) ◽  
pp. 231-236
Author(s):  
Navid Noroozi ◽  
Paknosh Karimaghaee ◽  
Ali Akbar Safavi ◽  
Amit Bhaya
Keyword(s):  
Neural Networks ◽  
Newton Method ◽  
Finite Time ◽  
Continuous Newton Method
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