算子方程

In Chapter 2,we firstly study the super-stability of the exponential operator equation f= ff in some special spaces.

第二章首先研究了指数算子方程f=ff在一些特殊空间中的超稳定性问题。

Then we consider the stability of the exponential operator equation under the definition which Ger first defined.

接着我们又讨论了在Get提出的稳定性意义下，指数算子方程稳定性的一些情况。

Gradient regularization method ; Frechet derivative ; regularization parameters ; parameter identification ; ill posedness ; elliptic operator equation

梯度正则化方法； Frechet导数；正则参数；参数识别；不适定；椭圆算子方程

Moreover,theε-Hyers-Ulam stability of the general operator equation is introduced.Some properties of this kind of stability are discussed.

并且由此给出了一般的算子方程的ε-Hyers-Ulam稳定性，对这种稳定性进行了初步的讨论。

According to fifteen sorts of eigenvalues,the specific solution to a type of homogeneous equation with harmonic operator of six steps polynomial in cylindrical coordinate is obtained by the variable method, and the method of determining the constant is given.

对圆柱坐标系下齐次6阶"多项式"形式的调和算子方程，按本征值分15种情况分别给出了其分离变量解的具体形式，给出常数的确定方法；并将结果推广到各种非齐次情况和非轴对称情况。

It has been prepared for the investigation of inexact quasi-newton method for operator equations in infinite dimensional space.

文献[1]对有限维空间中非线性方程组的不精确拟牛顿法的收敛性进行了研究，为无穷维空间上的算子方程的不精确拟牛顿法的研究作好了准备。

Inverse problems ; nonlinear ill-posed operator equations ; Newton type method ; implicit iterative method ; iteration stopping rule

反问题；非线性不适定算子方程； Newton型方法；隐式迭代法；迭代终止准则

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

A three solutions theorem of nonlinear operator equation in Hilbert space was given by Sun Jing-xian in 1983,in this paper,the theorem was expanded to general Banach space by using gradient method ,and some conditions was weakened,such as the local Lipschitz condition s transformation to the bounded character of F and so on.

依据H ilbert空间中非线性算子方程的一个三解定理，本文运用最速下降法将这个定理推广到了一般的Banach空间，并且减弱了原定理的某些条件，如将局部Lipschitz条件减弱为F的有界性等

In this paper, nonnegative matrix and operator equation have been discussed.

本文研究的内容分别涉及到非负矩阵和算子方程的有关内容。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。