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51.
L. O. Jay 《BIT Numerical Mathematics》2001,41(2):422-429
To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q [1,+] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
52.
Song-bai Sheng 《计算数学(英文版)》2001,(6)
1. IntroductionConsider the following nonsmooth equationsF(x) = 0 (l)where F: R" - R" is LipsChitz continuous. A lot of work has been done and is bellg doneto deal with (1). It is basicly a genera1ization of the cIassic Newton method [8,10,11,14],Newton-lthe methods[1,18] and quasiNewton methods [6,7]. As it is discussed in [7], the latter,quasiNewton methods, seem to be lindted when aPplied to nonsmooth caJse in that a boundof the deterioration of uPdating matrir can not be maintained w… 相似文献
53.
54.
55.
Conjugate gradient methods are efficient methods for minimizing differentiable objective functions in large dimension spaces.
However, converging line search strategies are usually not easy to choose, nor to implement. Sun and colleagues (Ann. Oper.
Res. 103:161–173, 2001; J. Comput. Appl. Math. 146:37–45, 2002) introduced a simple stepsize formula. However, the associated convergence domain happens to be overrestrictive, since it
precludes the optimal stepsize in the convex quadratic case. Here, we identify this stepsize formula with one iteration of
the Weiszfeld algorithm in the scalar case. More generally, we propose to make use of a finite number of iterates of such
an algorithm to compute the stepsize. In this framework, we establish a new convergence domain, that incorporates the optimal
stepsize in the convex quadratic case.
The authors thank the associate editor and the reviewer for helpful comments and suggestions.
C. Labat is now in postdoctoral position, Johns Hopkins University, Baltimore, MD, United States. 相似文献
56.
This paper deals with the boundedness in probability and convergence for solutions of stochastic Liénard-type equations. Some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained. We also show that white noise can affect the boundedness of corresponding deterministic Liénard equations. 相似文献
57.
Maolin Pan 《Insurance: Mathematics and Economics》2008,42(1):119-126
In this paper, we investigate the problems of convergence of experience-based ratemakings regarding the Esscher principle. In addition to the Bayes and the classical credibility premiums, we suggest a new credibility formula for the Esscher premium. Then we show the convergence of the Bayes and the newly defined credibility premiums towards the individual premium and point out that the classical credibility premium does not generally converge to the individual premium by presenting a sufficient and necessary condition under which the classical credibility Esscher premium converges to the individual premium. A simulation study is carried out to illustrate the theoretical conclusions. 相似文献
58.
A kind of function-valued Padé-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced on the polynomial space and an algorithm is sketched by means of the formal orthogonal polynomials. This method can be applied to approximate characteristic values and the corresponding characteristic function of Fredholm integral equation of the second kind. Moreover, theoretical analyses show that FPTAVOP method is the most effective one for accelerating the convergence of a sequence of functions. In addition, a typical numerical example is presented to illustrate when the estimates of characteristic value and characteristic function by using this new method are more accurate than other methods. 相似文献
59.
Nikodem Mro?ek 《Journal of Mathematical Analysis and Applications》2009,349(2):452-458
We introduce the notion of equi-ideal convergence and use it to prove an ideal variant of Egorov's theorem. We also show that this variant usually cannot be strengthen to a direct analogue of Egorov's theorem. 相似文献
60.
The approximate solvability of a generalized system for relaxed cocoercive mixed variational inequality is studied by using the resolvent operator technique. The results presented in this paper are more general and include many previously known results as special cases. 相似文献