It is often useful to replace a function with a sequence of smooth functions
approximating the given function to resolve minimizing optimization problems.
The most famous one is the Moreau envelope. Recently the function was organized
using the Br
egman distance h D . It is worth noting that Bregman distance h D is
not a distance in the usual sense of the term. In general, it is not symmetric and it
does not satisfy the triangle inequality
The purpose of the research is to study the convergence of the Moreau envelope
function and the related proximal mapping depends on Bregman Distance for a
function on Banach space. Proved equivalence between Mosco-epi-convergence of
sequence functions and pointwise convergence of Moreau-Bregman envelope We
also studied the strong and weak convergence of resolvent operators According to
the concept of Bregman distance.
Nonlinear conjugate gradient (CG) method holds an important role in solving large-scale unconstrained optimization problems. In this paper, we suggest a new modification of CG coefficient �� that satisfies sufficient descent condition and possesses global convergence property under strong Wolfe line search. The numerical results show that our new method is more efficient compared with other CG formulas tested.
Conjugate gradient algorithms are important for solving unconstrained optimization
problems, so that we present in this paper conjugate gradient algorithm depending on
improving conjugate coefficient achieving sufficient descent condition and globa
l
convergence by doing hybrid between the two conjugate coefficients [1] and
[2]. Numerical results show the efficiency of the suggested algorithm after its
application on several standard problems and comparing it with other conjugate gradient
algorithms according to number of iterations, function value and norm of gradient vector.
In this thesis, we review the problems of instructors’ assessment and propose some solutions in the context of an assistant system for the evaluation of instructors in higher education institutions, and implement this system at the University of kala
moon as a practical case with real data to verify results.
This research aims to prove the possibility of a flexible system in selecting instructors’ evaluation criterias in accordance with the chosen institution, and in the objectivity and impartiality of the assessment of instructors and the accuracy and the consistency of decision makers' opinions.
In this paper, spline technique with five collocation parameters for finding the
numerical solutions of delay differential equations (DDEs) is introduced. The presented
method is based on the approximating the exact solution by C4-Hermite spline
i
nterpolation and as well as five collocation points at every subinterval of DDE.The study
shows that the spline solution of purposed technique is existent and unique and has
strongly stable for some collocation parameters. Moreover, this method if applied to test
problem will be consistent, p-stable and convergent from order nine .In addition ,it
possesses unbounded region of p-stability. Numerical experiments for four examples are
given to verify the reliability and efficiency of the purposed technique. Comparisons show
that numerical results of our method are more accurate than other methods.
In this article, we propose a powerful method called
homotopy perturbation method (HPM) for obtaining the
analytical solutions for an non-linear system of partial
differential equations. We begin this article by apply HPM
method for an important models of linear and non-linear
partial differential equations.
In this paper, spline approximations with five collocation points are used for the
numerical simulation of stochastic of differential equations(SDE). First, we have modeled
continuous-valued discrete wiener process, and then numerical asymptotic st
ochastic
stability of spline method is studied when applied to SDEs. The study shows that the
method when applied to linear and nonlinear SDEs are stable and convergent.
Moreover, the scheme is tested on two linear and nonlinear problems to illustrate
the applicability and efficiency of the purposed method. Comparisons of our results with
Euler–Maruyama method, Milstein’s method and Runge-Kutta method, it reveals that the
our scheme is better than others.
The aim of this paper is to study and generalize some results that related by the complete continuity of the urysohn.s operator of two variables on a set on which a lebesgue meagure is defined and study uniform convergence sequence of the urysohn .s.
operators that defined by functions using convergence meager Depending on caratheodory condition of measurable sets .
In this paper, an iterative numerical method for obtaining approximate values of
definite single, double and triple integrals will be illustrated. This method depends on
approximating the single integral function by spline polynomial of fifth degre
e, while
Gauss Legendre points as well as spline polynomials are used for finding multiple
integrals.
The study shows that when the method are applied to single integrals is convergent
of order sixth, as well as when applied to triple integrals is convergent of order sixth for
three Gauss Legendre points or greater.
Errors estimates of the proposed method alongside numerical examples are given to
test the convergence and accuracy of the method.
In this work we study the convergence of Haar- Series
with real monotone coefficients and find the sum of that
series using the generalized liner summing mothed. For we
use the special classes.
