On the efficiency of a modification of newton’s method of solving a system of equations

1995 ◽  
Vol 73 (5) ◽  
pp. 600-601
Author(s):  
S. N. Perfllov ◽  
R. N. Sattarov
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
System Of Equations

Formal proofs for theoretical properties of Newton's method

2011 ◽  
Vol 21 (4) ◽  
pp. 683-714 ◽  
Author(s):  
IOANA PAŞCA
Keyword(s):  
Multivariate Analysis ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Algorithms ◽  
System Of Equations ◽  
Proof Assistant ◽  
Formal Proofs ◽  
Original Result ◽  
Accurate Model ◽  
Formal Study

We discuss a formal development for the certification of Newton's method. We address several issues encountered in the formal study of numerical algorithms: developing the necessary libraries for our proofs, adapting paper proofs to suit the features of a proof assistant and designing new proofs based on the existing ones to deal with optimisations of the method. We start from Kantorovitch's Theorem, which gives the convergence of Newton's method in the case of a system of equations. To formalise this proof inside the proof assistant Coq, we first need to code the necessary concepts from multivariate analysis. We also prove that rounding at each step in Newton's method still yields a convergent process with an accurate correlation between the precision of the input and that of the result. This proof is based on Kantorovitch's Theorem, but is an original result. An algorithm including rounding is a more accurate model for computations with Newton's method in practice.

Computation of the Pressure Distribution in Hydrodynamic Bearings Using Newton’s Method

2004 ◽  
Vol 126 (2) ◽  
pp. 404-407 ◽  
Author(s):  
Lars Johansson and ◽  
Ha˚kan Wettergren
Keyword(s):  
Pressure Distribution ◽  
Newton Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Reynolds Equation ◽  
Usual Sense ◽  
System Of Equations ◽  
Equilibrium Equations ◽  
Hydrodynamic Bearings

In this paper an algorithm is developed where Reynolds’ equation, equilibrium equations and non-negativity of pressure are formulated as a system of equations, which are not differentiable in the usual sense. This system is then solved using Pang’s Newton method for B-differentiable equations.

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.

scholarly journals A Hybrid Approach for Solving Systems of Nonlinear Equations Using Harris Hawks Optimization and Newton’s Method

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Rami Sihwail ◽  
Obadah Said Solaiman ◽  
Khairuddin Omar ◽  
Khairul Akram Zainol Ariffin ◽  
Mohammed Alswaitti ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Hybrid Approach ◽  
Systems Of Nonlinear Equations
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