Newton methodnonlinear equations/ Newton-type methodsnonlinear equationsquadratic matrix groupsnumerical methodsmatrix Lie groupsLie algebraCayley approximantIn this paper we consider numerical methods for solving nonlinear equations on matrix Lie groups. Recently Owren and Welfert (Technical Report Numerics, ...
We consider the system of nonlinear equations H(x) = 0; x 2 D ae R m : (1) If H is Fr'echet differentiable, then the standard technique for finding a solution of (1) is the generalized Newton's method due to Ben-Israel [5]: x k+1 = x k Gamma H 0 (x k ) + H(x k...
(View the complete code for this example.) This example solves a nonlinear system of equations by Newton’s method. Let the nonlinear system be represented by where is a vector and F is a vector-valued nonlinear function. Newton’s method is an iterative technique. The method starts with ...
Newton iterative method is an important and commonly used iterative methods for solving nonlinear equations. 翻译结果2复制译文编辑译文朗读译文返回顶部 正在翻译,请等待... 翻译结果3复制译文编辑译文朗读译文返回顶部 Solving nonlinear equations of Newton iteration method is an important and common iteration ...
. 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.....
In this paper, we present a simple, and yet powerful and easily applicable scheme in constructing the Newton-like iteration formulae for the computation of the solutions of nonlinear equations. The new scheme is based on the homotopy analysis method applied to equations in general form equivalent...
Several methods are discussed for solving nonlinear equations F(u) = f, where F is a monotone operator in a Hilb... N. S.hoang,A. G.ramm - Asian-European Journal of Mathematics 被引量: 60发表: 2009年 An extension of the Newton-Kantorovi method for solving nonlinear equations with an...
A subspace linesearch strategy for the globalization of Newton-GMRES method is proposed. The main feature of our proposal is the simple and inexpensive way we determine descent directions in the low-dimensional subspaces generated by GMRES. Global and lo
Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian For solving large systems of nonlinear equations by quasi-Newton methods it may often be preferable to store an approximation to the Jacobian rather than a... L.,K.,Schubert - 《Math Comp》 被引量: 288发表...
This method has an advantage over Newton's methods since it avoids solving approximate Jacobian equations. Under some mild assumptions, we show that the ... SW Vong,ZJ Bai,XQ Jin,... 被引量: 9发表: 2011年 Local convergence of Newton-like methods for degenerate eigenvalues of nonlinear eigen...