This paper aims at developing two versions of the generalized Newton method to compute local minimizers for nonsmooth problems unconstrained and constrained optimization that satisfy an importan...

Iterative regularization methods for nonlinear ill-posed equations of the form F (x) = y, where F : D(F ) ⊂ X → Y is an operator between Hilbert spaces X and Y , usually involve calculation of the Fréchet derivatives of F at each iterate and at the unknown solution x†. In this paper, we suggest a modified form of the generalized Gauss-Newton method which requires the Fréchet derivative of F onl...

The dogleg method is a classical trust-region technique for globalizing Newton’s method. While it is widely used in optimization, including large-scale optimization via truncatedNewton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexac...

Sequential testing procedures are developed for the parameters of generalized life distributions. Robustness of the testing procedures is studied, when the distribution under consideration has undergone a change. In order to apply Newton-Raphson method for the purpose of plotting the operating characteristic (OC) and average sample number (ASN) functions, a method of choosing the initial values...

In this paper we describe a fast multilevel algorithm for the solution of a system of nonlinear integrodifferential equations that model steady-state combined conductive-radiative heat transfer in two space dimensions. This extends our previous work in one space dimension. We formulate the equations as a compact fixed point problem with the temperature as the unknown. The fixed point map requir...

‎in this paper‎, ‎we present a new modification of chebyshev-halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎the convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎so‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that o...

Presently there is a little information that relates to heat shield systems.  Also this information is not certain in so many cases.  The main reason is that accurate calculations for measuring the sacrificing rate of various materials have not been obtained yet.  Additionally, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test...

In this paper, we present a hybrid method for the solution of a class of composite semismooth equations encountered frequently in applications. The method is obtained by combining a generalized finite difference Newton method to a inexpensive direct search method. We prove that, under standard assumptions, the method is globally convergent with a local rate of convergence which is superlinear o...

We present and analyze a new damping approach called backward step control for the globalization of the convergence of Newton-type methods for the numerical solution of nonlinear root-finding problems. We provide and discuss reasonable assumptions that imply convergence of backward step control on the basis of generalized Newton paths in conjunction with a backward analysis argument. In particu...