查询词典 operator equation

To sum up, in the paper unified computational methods for solving notwell-posed continuous linear operator equation wore given and there are alsoconvenient for the physical problems.

综上所述，本文中关于不适定连续线性算子方程求解问题的研究，注意到各种物理问题求解的方便性，给出了解决此类问题的统一的计算方法。

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

According to some practical examples, this thesis gives the basic definition and uniform form of inverse problems and ill-posed problems, and then operator equation is got by discursion.

本文从一些实例出发，给出了反问题和不适定问题的基本概念及反问题的统一形式，从而得出了算子方程。

And to solve the linear problem is turned to obtain the solution of an operator equation equivalent to it.

相应线性方程的带积分边值条件的混合问题，则是通过求解与线性方程等价的算子方程解决的。

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。

Firstly, by constructing the Lyapunov function with a special structure, a prior estimate is obtained. Secondly, with the help of Green\'s function, the original problem is transformed into an equivalent operator equation, and the fixed point theory of contraction mapping in a Banach space guarantees the existence and uniqueness of the global solution.

首先，构造具有特殊结构的Lyapunov函数，得到解的先验估计；其次，借助Green函数将原方程等价变换成算子方程，Banach压缩映射的不动点定理保证了全局解的存在唯一性；最后通过常微分方程的定解，证明了主要结论，即平凡解全局渐近稳定。

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。

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

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。