اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA robust Kantorovichs theorem on inexact Newton method with relative residual error tolerance
189
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges Q-linearly to a zero of the non-linear operator under consideration. Using this result we show that Newton method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance. In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on Newton method.
قيم البحث
اقرأ أيضاً
In this work we present a simplifyed proof of Kantorovichs Theorem on Newtons Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.
We propose a inexact Newton method for solving inverse eigenvalue problems (IEP). This method is globalized by employing the classical backtracking techniques. A global convergence analysis of this method is provided and the R-order convergence prope
rty is proved under some mild assumptions. Numerical examples demonstrate that the proposed method is very effective for solving the IEP with distinct eigenvalues.
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold fo
r a large class of discretizations. Efficiency of the error estimate is shown for a natural discretization of low order. Numerical examples confirm the theoretical results. The resulting adaptive mesh refinement procedures in 3d recover the adaptive convergence rates known for elliptic problems.
We first investigate properties of M-tensor equations. In particular, we show that if the constant term of the equation is nonnegative, then finding a nonnegative solution of the equation can be done by finding a positive solution of a lower dimensio
nal M-tensor equation. We then propose an inexact Newton method to find a positive solution to the lower dimensional equation and establish its global convergence. We also show that the convergence rate of the method is quadratic. At last, we do numerical experiments to test the proposed Newton method. The results show that the proposed Newton method has a very good numerical performance.
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, whi
ch relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
