扰动

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

The uniform bounded stable condition of the residual and its to nonlinear perturbations are proved by using Lyapunov function and uniform bounded lemma.

并利用Lyapunov函数和一致有界引理证明了故障检测残差信号的一致有界稳定条件和对非线性扰动的鲁棒性。

We show that in error estimates,the condition number 〓 of any invertiblelinear bounded operator T in Banach spaces is minimal.

第III部分考虑条件数在Banach空间中扰动分析的极小性质。

Let 〓 be two Hilbert spaces over the same field,and let T:〓a bounded linear operator with closed range.

在1.4中，我们在最一般条件假设下，给出了Hilbert空间上线性有界算子及其最小二乘解的误差分析，从而完整地解决了Hilbert空间算子的扰动理论。

Simultaneously, we identify that the perturbation of these operators by a small norm operator is still nonwandering; further, we can obtain the theory that every bounded linear operator can be decompositioned into nonwandering operators.

同时，证明了这些算子经一小扰动后，可保持它们的非游荡性不变；进而可获得有界线性算子关于非游荡算子的分解理论。

Let Xand Y be different Banach spaces and 〓Lbe a bounded linear operator,thegeneralized condition number 〓and〓ABA=A,B〓L}are studied.

文章讨论了两类广义条件数的几种表达式，研究了这两类广义条件数之间的关系，并将它们用到算子方程的扰动估计中，推广了Demko[IV.1]中的结果。

Medium asymmetry makes clear broomrape of actual GDP foreword to disturb to be had in the different level of economic cycle randomly those who differ is durative with the fluctuation, because this arranges cycle and the economic policy that oppose cycle,have distinct effect effect.

实际GDP序列当中的非对称性表明随机扰动在经济周期的不同阶段具有不同的持续性和波动性，因此顺周期与反周期的经济政策具有不同的作用效果。

At very small scales, the disturbances caused by the random motion of molecules in a liquid is called Brownian motion.

在非常小的尺度上，由液体中的分子随机运动造成的扰动被称为布朗运动。

This paper presents a kind of nonlinear adaptive inverse control with -filtered algorithm, which has adaptive disturbance canceler and feedback compensation in it.

提出了一种带自适应扰动消除器和反馈补偿的非线性自适应逆控制系统。

This method consists of solving a Cauchy problem for a linear operator equation.

3，4」中，提出了解右端数据有扰动的线性算子方程的动态系统方法·实际间题中，算子与右端数据通常是近似已知的。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。