The structure of this paper is organized as follows:In the first chapter we survey the history of conjugate gradient method ,and discuss five conjugate gradient methods respectively which are FR method ,PRP method ,HS method ,CD method ,DY method . They are currently considered to be well-known methods for large scale unconstrained optimization problems.
In Chapter 2, the author proposes two new dependent Fletcher-Reeves conjugate gradient methods arising from different choice for the scalarβk and make two different kinds ofestimations of upper bounds of \βk \ with respect to βkFR, which are based on Abel Theorem of non-convergent series of positive items.
In Chapter 5, the author investigates the global convergence properties of the FR and PRP conjugate gradient methods using the two Armijo-type line searches proposed in Chapter 4. Further, the author investigates the global convergence of the conjugate gradient methods with the negative βk under the two Armijo-type line searches.
In this paper, we take a little modification to the Fletcher-Reeves (FR) method such that the direction generated by the modified method provides a descent direction for the objective function.
Moreover, the modified method reduces to the standard FR method if line search is exact.
The frequency response (FR) method has been applied to study the dynamics of cyclopropane adsorption in faujasite, mordenite, beta and ZSM-5 zeolites containing Br?nsted or Lewis acid sites in the concentration range of 0.586-0.772 meq/g.
One of the characteristic examples of the inability of the classical linear frequency response (FR) method to identify the correct kinetic mechanism is adsorption of some substances (p-xylene, 2-butane, propane or n-hexane) on silicalite-1.
A valuable feature of the FR method, at least for simple systems, is the relative position of the in-phase and out-of-phase spectral components.
This paper presents a new method, FR method, to solve the inverse problems of acoustic wave equations. FR method is a general numerical inversion algorithm of acoustic wave equations. It can be used to one, two or three dimensional inverse problems with any different boundary conditions. The basic principle and formulae are derived carefully in the paper, and numerical examples of one and two dimensional inverse problems are given. The numerical results show the accuracy and stability of the method.