Weaker convergence for Newton's method under Hölder differentiability

We use more precise majorizing sequences than in earlier studies such as [J. Appell, E. De Pascale, J.V. Lysenko, and P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997), pp. 1–17; I.K. Argyros, Concerning the ‘terra incognita’ between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005), pp. 179–194; F. Cianciaruso, A further journey in the ‘terra incognita’ of the Newton–Kantorovich method, Nonlinear Funct. Anal. Appl. 15 (2010), pp. 173–183; F. Cianciaruso and E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003), pp. 713–723; F. Cianciaruso, E. De Pascale, and P.P. Zabrejko, Some remarks on the Newton–Kantorovich approximations, Atti Sem. Mat. Fis. Univ. Modena 48 (2000), pp. 207–215; E. De Pascale and P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998), pp. 271–280; J.A. Ezquerro and M.A. Hernández, On the R-order of convergence of Newton's method under mild differentiability conditions, J. Comput. Appl. Math. 197 (2006), pp. 53–61; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations (in Russian), Dokl. Akad. Nauk BSSR 38 (1994), pp. 20–24; P.D. Proinov, New general convergence theory for iterative processes and its applications to Newton–Kantorovich type theorems, J. Complexity 26 (2010), pp. 3–42; J. Rokne, Newton's method under mild differentiability conditions with error analysis, Numer. Math. 18 (1971/72), pp. 401–412; B.A. Vertgeim, On conditions for the applicability of Newton's method, (in Russian), Dokl. Akad. N., SSSR 110 (1956), pp. 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957), pp. 166–169 (in Russian); English transl.: Amer. Math. Soc. Transl. 16 (1960), pp. 378–382; P.P. Zabrejko and D.F. Nguen, The majorant method in the theory of Newton–Kantorovich approximations and the Pták error estimates, Numer. Funct. Anal. Optim. 9 (1987), pp. 671–684; A.I. Zinc?enko, Some approximate methods of solving equations with non-differentiable operators (Ukrainian), Dopovidi Akad. Nauk Ukraïn. RSR (1963), pp. 156–161] to provide a semilocal convergence analysis for Newton's method under Hölder differentiability conditions. Our sufficient convergence conditions are also weaker even in the Lipschitz differentiability case. Moreover, the results are obtained under the same or less computational cost. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.     

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Generalizations of Hölder’s and some related inequalities

In this paper we establish some new generalizations and refinements of Hölder’s inequality and some related inequalities. We also show that many existing inequalities related to the Hölder inequality are special cases of the inequalities presented.     

Where is it?Just here!

Where is it是一个全32位的软件,运行于Windows95/98/NT之下,它能够帮助你将你的文件按照不同的类型范围划分,你还可以自己定义划分的类型或范围;同时它能支持各种格式的文件,还能支持直接浏览各种常用格式的压缩包,如ZIP,ARJ,RAR,CAB,TAR,ZOO等;内建的搜索功能,可以帮助你在最短的时间内找出你需要的文件来,并且可以实     

Security flaw of Hölbl et al.’s protocol

Recently, Hölbl et al. [M. Hölbl, T. Welzer, B. Brumen, Improvement of the Peyravian–Jeffries’s user authentication protocol and password change protocol, Computer Communications 31 (2008) 1945–1951] have proposed an improvement of Peyravian–Jeffries’s user authentication protocol and password change protocol [M. Peyravian, C. Jeffries, Secure remote user access over insecure networks, Computer Communications 29 (5–6) (2006) 660–667]. Peyravian–Jeffries’s scheme suffers from an active off-line password-guessing attack [J. Munilla, A. Peinado, Off-line password-guessing attack to Peyravian–Jeffries’s remote user authentication protocol, Computer Communications 30 (1) (2006) 52–54], and Hölbl et al. state that their improved protocol overcomes this weakness. However, we show in this paper that although this proposed protocol prevents this active attack, it remains vulnerable to a passive (simpler) off-line password-guessing attack.     

Convergence rate of the Levenberg-Marquardt method under Hölderian local error bound

ABSTRACT

In this paper, we study the convergence rate of the Levenberg-Marquardt (LM) method under the Hölderian local error bound condition and the Hölderian continuity of the Jacobian, which are more general than the local error bound condition and the Lipschitz continuity of the Jacobian. Various choices of the LM parameter are also discussed.     

On a non-smooth version of Newton's method based on Hölderian assumptions

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in Banach space using Newton's method. The differentiability of the operator involved is not assumed, and we use Hölderian assumptions. We provide a semilocal convergence analysis based on a suitable point-based approximation. Our approach is justified by numerical examples where our results apply, whereas earlier ones cannot be applied in this way.     

Back pain in school children--where to from here?

Back pain is now recognised to occur early in childhood and is associated with high prevalence rates when estimated by survey. This review paper considers the risk factors associated with back pain in children aged 11-14 years, and particularly those present in a school setting. The risk factors most significantly associated with back pain are primarily characteristics of the individual with less strong associations with factors present in the school environment. The majority of intervention studies undertaken in a school setting have focussed on the effect of school furniture on posture and comfort and were of short-term duration. There is a need for further research in order to achieve a better understanding of the risk factors present in a school environment and to address ways to reduce the currently recognised perceived problem of back pain among school children. A strategy for an evidence-based longitudinal intervention study is proposed, with the content outlined under the headings: policy, school equipment and furniture, individual and family.     

Worst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients

The worst-case behaviour of a general class of regularization algorithms is considered in the case where only objective function values and associated gradient vectors are evaluated. Upper bounds are derived on the number of such evaluations that are needed for the algorithm to produce an approximate first-order critical point whose accuracy is within a user-defined threshold. The analysis covers the entire range of meaningful powers in the regularization term as well as in the Hölder exponent for the gradient. The resulting complexity bounds vary according to the regularization power and the assumed Hölder exponent, recovering known results when available.     

Musiktauschbörsen

Im Informatik-Spektrum 1/2004 haben Steinmetz und Wehrle Peer-to-Peer-Systeme vorgestellt. Ein wichtiges Anwendungsfeld derartiger Systeme sind Tauschbörsen für Musik. Die Musikindustrie erleidet seit einigen Jahren massive Umsatzrückgänge und führt dies insbesondere auf die Tauschbörsen zurück. Nachfolgend werden konventionelle und innovative Ansätze zur Lösung dieses Problems skizziert.     

附录H H4400计算机系统

H4400是具有自动重新组合能力的模块多处理机,它配备了重新分配资源用的软件(SHOC控制系统)。这种系统是由存贮器/处理器开关(MPS)把各独立模块连接在一起组合而成的。模块类型:运算和控制处理器(A-CP)模块、输入/输出处理器(IOP)模块、专用     

漫步者H500/H110

2004年,漫步者除了推出了许多新款音箱产品外．还推出了数款耳机产品．H500是其中一款头戴式产品。这款产品较目前市面上销售的各种耳机产品而言．外形显得有些朴素．但“人不可貌相”．H500在设计上有许多亮点。     

技嘉H55m-UD2H主板

低功耗、内置显卡是新Corei5、Corei3的最大特点，确实从特性上看来新Core i5、Core i3非常适合HTPC，但是看到它们不俗的性能和巨大的超频潜力，谁又能说它们只能用于HTPC呢？     

精英H55H—M主板 整合主板H55挑大梁

虽然当前P55主板的价格在持续的下滑，但与i5—750这样的主流处理器搭配，最低的组合价格也在2400以上，而H55主板作为英特尔新一代的整合主板，突出的性价比却正是其最大的亮点。所以本期我们测试了H55芯片组主板中比较有代表意义的精英H55H-M主板，来展现H55在良好的性价比下的实际性能。     

H61也高效 精英H61H2-A2 Deluxe主板

尽管之前不被看好,但H61却是目前仍活跃在主流市场上的主力。精英最新的H61H2-A2 Deluxe主板证明了H61不仅性价比高同时也能拥有高规格。产品采用了全尺寸PCB板设计,配备4+2相供电电路,能有效满足Ivy Bridge架构处理器的供电需求。     

Numerische Lösung von Anfangswertaufgaben gewöhnlicher Differentialgleichungen n-ter Ordnung

In the present paper a new method is given for the numerical treatment of the initial problemsy ⁽ⁿ⁾=f(x,y,y′, ...,y ^(n?1),y ⁽ⁱ⁾ (x _o )=y _o ⁽ⁱ⁾ , i=0, 1, ...,n?1. This method is an one-step process of order four. For a class of linear differential equations the exact solution is obtained. Moreover some numerical results are presented.