Newton methodnonlinear equations/ Newton-type methodsnonlinear equationsquadratic matrix groupsnumerical methodsmatrix Lie groupsLie algebraCayley approximantIn this paper we consider numerical methods for solv
Nonlinear equationsNew quasi-Newton equationModified quasi-Newton methodLocal superlinear convergenceIn this paper, a modified quasi-Newton method is proposed for solving the nonlinear equation F(x)=0 F ( x ) = 0 mathContainer Loading Mathjax , which is based on a new quasi-Newton approach. ...
We present and analyze a modified seventh-order convergent Newton-type method for solving nonlinear equations. The method is free from second derivatives. Some numerical results illustrate that the proposed method is more efficient and performs better than the classicalNewton's method.Liang Fang...
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A class of Newton-HSS methods was established by Bai and Guo (2010) to solve the nonlinear equations whose Jacobian matrices are large sparse and positive definite at the exact solution points. The inexact Newton-MHSS method was proposed by Yang and Wu (2012) for solving the large sparse ...
Martínez, J.M., Zambaldi, M.: An inverse column-updating method for solving large-scale nonlinear systems of equations. Optim. Methods Softw. 1(2), 129–140 (1992) Article Google Scholar Morini, B., Porcelli, M.: TRESNEI, a Matlab trust-region solver for systems of nonlinear equaliti...
. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. Solving Nonlinear Equations w.....
Master the Newton-Raphson Method for solving nonlinear systems of equations in a 5-minute video lesson. Enhance your numerical analysis skills and take a quiz!
Interior point methods (IPM) rely on the Newton method for solving systems of nonlinear equations. Solving the linear systems which arise from this approach is the most computationally expensive task of an interior point iteration. If, due to problem’s inner structure, there are special techniques...
The new method becomes fast and able to calculate more nonlinear eigenpairs. Numerical experiment confirms these two progresses. Also, the MP-Newton method inherits the advantages of the minimax method. A convergence result for the method is established. Finally, an application for solving a ...